# A Theory of Exchange Rates and the Term Structure of Interest Rates

Save this PDF as:

Size: px
Start display at page:

Download "A Theory of Exchange Rates and the Term Structure of Interest Rates"

## Transcription

5 78 Hyoung-Seok Lim an Masao Ogaki are perfect substitutes an o not nee to be istinguishe. The omestic short- an long-term bons are iscount bons paying one unit of the omestic currency after one perio an two perios, respectively. The foreign bons behave in the same manner. At time t, a representative investor allocates his/her initial wealth W t among the three assets an he/she collects the payoffs pai by the assets he hols at the beginning of time t + 1. Let q t be the price of omestic long-term bons at time t. Let r t be the omestic short-term interest rate, an let R t be the omestic long-term interest rate. Then, the rate of return on holing omestic long-term bons for one 1 1 perio (r L, t) is q 1 t. Since qt =, we have r q + r Lt, = ( 1+ Rt) ( 1+ R ) t 1 t Rt rt + rt ( + Rt) The risk premium for omestic long-term bons (r L, t) is efine to be the ifference between the expecte rate of return on holing long-term bons for one perio an the rate of return for short-term bons. Thus, we have: ( ) 1 { ( )} 1, () ρ Lt, = E t r Lt, r t R t r t + E t r t + where E t is the expectation operator conitional on the information set in perio t, W t. We assume that W t inclues the current an past values of r t, R t, r t *, R t *, an s t, where r t *, an R t * are the foreign short- an long-term interest rates, respectively, an s t is the natural log of the exchange rate expresse in terms of the omestic currency. The rate of return on holing foreign bons for one perio in terms of the omestic currency (r F,t) is rt* + st+1 st. Let the risk premium for foreign bons (r F,t) enote the ifference between the expecte rate of return on holing foreign bons for one perio an the rate of return for short-term bons. Then, ρ Ft, = E t ( r F, t) r t = r t * + E t ( s t +1 ) s t r t. The moel assumes that, at time t, a representative investor with a constant absolute risk aversion utility function maximizes his/her expecte utility of wealth at the kw e t +1 beginning of the time t + 1(= W t+1) subject to a buget constraint; max Et k, s.t. Wt = BS, t + BLt, + BFt,, where k is the coefficient of absolute risk aversion, an enotes eman, so that omestic currency amounts investe in omestic short-, longterm, an foreign bons are B St,, B Lt, an B Ft,, respectively. W t is the initial wealth at time t, an the value of an investor s assets at the beginning of time t + 1, W t+1, satisfies: Wt+ 1 = BS, t( 1+ rt) + BL, t( 1+ rlt, ) + BF, t( 1+ rft, ). In the partial equilibrium moel, the stochastic processes for the interest rates are exogenously given, an the utility function is parameterize. The equilibrium s exchange rate satisfies the foreign bons market clearing conition, BFt, = BFt,, where s B Ft, is the supply of foreign bons to the omestic resients. It is assume to be equal to the cumulative current account balance an to follow the ynamic equation: s s BFt, = BFt, 1 + Ct. An, C t is the current account balance in perio t that satisfies: Ct = a+ b St + ut, where b is a positive number, an u t is a trae shock which is assume to be white noise with variance σ u. Suppose that W t+1 is normally istribute conitional on W t an that the measure of the absolute risk aversion, k, is a positive constant. Uner these assumptions, a representative investor s optimization problem is equivalent to maximizing: t

6 EXCHANGE RATES AND THE TERM STRUCTURE OF INTEREST RATES 79 k max ( ) var ( ) { B,, B E, } t Wt+ 1 t Wt+ 1, where Et( Wt+ 1) = Wt( 1+ rt) + BL, t( ρlt, ) + BF, t( ρft, ) Ft Lt an var t( Wt ) ( BL, t) var t( rt ) ( BF, t) var t( st ) ( BL + 1 = , t)( BFt, )cov t( rt+ 1, st+ 1 ). Firstorer conitions with respect to B Ft, an B Lt, are ρ Ft, kb ( Ft, )var t( st+1) + kb ( Lt, )cov t( rt+ 1, st+ 1)= 0 an ρ Lt, kb ( Lt, )var t( rt+ 1) + kb ( F, t)cov t( rt+ 1, st+ 1) = 0, respectively. Solving for B Ft, an B Lt, yiels the eman functions for foreign bons an omestic long-term bons, respectively. In particular, the eman for the foreign bon is: B Ft, ρft, ρlt, ψ ρft, ψ φ ρlt, [, ] =. (3) An, the eman for the omestic long-term bon is: s B Lt, ρft, ρlt, ψ φ ρft, ψ σ = + Lt, σ ρ r [, ]. (4) Here, ψ = 1 k σ 1 s ( cor ), φ = 1 cov, σ σ = s E t [ s t + 1 E t ( s t + 1)], σ r = r Et[ rt+ 1 Et( tt+ 1)] 1, cov, = E t[{s t+1 - E t(s t+1)}{r t+1 - E t(r t+1)}], an cor = cov, σ s σr respectively. The eman function for foreign bons, equation (3), epens on both the conitional covariance between the exchange rate an the short-term interest rate (cov) an the conitional variance of the exchange rate ( σ s ). At the same time, the stochastic processes of the exchange rate an cov also rely on the eman function for foreign bons. Therefore, in orer to solve for a rational expectations equilibrium, the values of cov an σ s must be consistent with the stochastic process of the exchange rate implie by the eman function for foreign bons. When the short-term interest rate rises, there are two opposite effects on the eman for foreign bons given the secon moments of the exchange rate an the short-term interest rate. These effects are the irect an inirect risk premium effects we efine in section 3. The irect risk premium effect is shown in the first term of equation (3). This effect is the change in the eman for foreign bons when the short-term interest rates rise, holing the risk premium for long-term bons constant. This effect is equal to -y an is negative. The inirect risk premium effect is the secon term of equation (3). This effect is the change in the eman for foreign bons when the short-term interest rate rises, holing the risk premium for foreign bons constant. This effect is equal to yf. In the rational expectations equilibrium erive in the next section, cov is negative, which implies that the inirect risk premium effect is positive. An intuitive explanation of the inirect risk premium effect is as follows: If the short-term interest rate unexpectely rises, the price of a long-term bon falls an long-term bon holers suffer an unexpecte capital loss. When cov is negative, the exchange rate tens to appreciate causing investors to suffer an aitional unexpecte loss if they hol foreign bons. Therefore, as long as an increase in the short-term interest rate is associate with an appreciation of the omestic currency, risk averse agents will want to avoi holing both long-term bons an foreign bons. When this association is stronger, investors are more willing to substitute between omestic long-term bons an foreign bons. In particular, when an increase in short-term interest rates reuces the risk premium for long-term bons, risk averse investors

7 80 Hyoung-Seok Lim an Masao Ogaki want to ajust their portfolios towar holing more foreign bons an fewer longterm bons. This inirect risk premium effect allows the eman for foreign bons to increase when the short-term interest rate rises. The existence of two opposite effects on the eman for foreign bons implies that the impact of a rise in the short-term interest rate on the eman for foreign bons epens on the relative strengths of these two effects. The inirect risk premium effect ominates the irect risk premium effect if an only if f > 1. Therefore, f coul be thought of as the relative magnitue of the inirect risk premium effect. In the next section, it will be shown that f is greater than 1 uner reasonable parameter configurations. The intuition for inirect an irect risk premium effects can be generalize with Ogaki (1990) s concepts of irect an inirect substitution effects to the cases of other utility functions an more than three assets. Given the secon moments, equations (3) an (4) give the eman functions for foreign bons an long-term bons, respectively, as functions of expecte returns. Hence it is possible to efine substitution an income effects for changes in expecte returns as in Blanchar an Plantes (1977) an Royama an Hamaa (1967). Because absolute risk aversion is assume to be constant, income effects o not appear in the eman for risky assets, notably foreign bons an long-term bons. Therefore, the price effects which appear in equations (3) an (4) are also the substitution effects. We can ecompose the substitution effect into irect an inirect substitution effects. Even though the inirect substitution effect is not equal to the inirect risk premium effect, the inirect risk premium effect ominates the irect risk premium effect if an only if the inirect substitution effect ominates the irect substitution effect. As we show in the next section, the inirect risk premium effect ominates with reasonable parameter values in our moel. In such cases, omestic short-term bons an foreign bons are complements. For the general utility function with any number of assets, a substitute of a substitute is always an inirect complement. In our moel, foreign bons an omestic longterm bons are substitutes, an both omestic short- an long-term bons are substitutes. This means that omestic short-term bons an foreign bons are inirect complements. 5. The Rational Expectations Equilibrium We use the moel presente in section 4 to erive the rational expectations equilibrium. The stochastic processes of interest rates are assume to be as follows: rt = μ+ et + ε, t (5) Rt = 1 + μ 1 + ( + c ) et, (6) 1 an r t * = μ, R * 1 t = + μ, where e t is a persistent interest rate shock an e t is a temporary interest rate shock. It is assume that e t follows an AR(1) process: e = ce + v, c <, (7) t t 1 t 1 an that it is inepenent of u t. It is also assume that e t, an v t are white noise with variance σ ε an σ v, respectively, an that they are inepenent of both each other an u t. 3 Finally, an m are positive numbers.

8 EXCHANGE RATES AND THE TERM STRUCTURE OF INTEREST RATES 81 It follows that: Et( rt+ 1) = μ + cet, (8) an from equation () an equation (8), ρlt, = εt. (9) For our purposes, we assume that the risk premium for long-term bons is non-zero. As shown in equation (9), the assumption employe here is that only e t is transmitte to the long-term interest rate, 4 so the risk premium is equal to the mean of the longterm interest rate plus a temporary interest rate shock. Define η σ ε =, which may be interprete as the measure of substitution between σ e both short- an long-term bons. If h = 0, then the risk premium for long-term bons will be the mean of the long-term interest rate, implying that the short- an the longterm bon will become more substitutable. The greater the magnitue of h, the smaller the egree of the substitution. Let L be the lag operator. Then, the equilibrium conition in perio t is, E[ A ( L) s ] = a+ D, t 0 t 0 (10) where A 0(L) =-yl -1 s + (b + y) an D0 = ut BF, t 1 ψφ ψet + ψ( φ 1) ε t. Taking conitional expectations with respect to W t on both sies yiels the equilibrium conition for perio t + 1: Et[ A( L) st+ 1] = a+ D1, (11) where A(L) =-yl -1 + (b + y) - yl an D 1 = y(1 - c)e t - y(f - 1)e t. Analogously, taking expectations conitional on W t on both sies yiels the equilibrium conition for any perio t = t, where t : Et[ A( L) st+ τ ] = a+ D, (1) where D = y(1 - c)e tc t-1. Solving equations (10), (11) an (1) as a ifference equation system of E t(s t+t) with respect to t provies the unique sale point solution for s t: s = s ( ) ( ) ( ) + 1 λ 1 λ s λ u B, 1 b b c e t λφ ( 1) εt, (13) 1 λ t t F t ( ) a where s 1 λ = φψ is the long-run equilibrium exchange rate that clears the b b current account, an ψ λ = 1+ b b 1+ 4 ψ ψ b. (14) It can be shown that 0 < l < 1, l/ y > 0, lim y 0l = 0, an lim y l = 1. Equation (13) shows that the investor s expecte values of cov an σ s affect the exchange rate ynamics through l an f. On the other han, the exchange rate

9 8 Hyoung-Seok Lim an Masao Ogaki ynamics in equation (13) imply certain values of cov an σ s, which nee to be consistent with the investor s expecte values in the rational expectations equilibrium. To analyze the equilibrium, we first solve for the rational expectation of cov. We then, show the uniqueness an existence of the equilibrium 5 by solving for the rational expectation of σ s. Before solving for the equilibrium, note the nature of equation (13). It explains the iscrepancy between actual an long-term equilibrium exchange rates through four factors: the trae shock at perio t, the cumulative current account balance, an, the persistent an temporary interest rate shocks. All factors, except the temporary interest rate shock, prouce effects consistent with the expecte irections. However, the temporary interest rate shock (e t) has a positive effect if the relative magnitue of the inirect risk premium effect, f, is greater than one. Calculating cov = E t[{s t+1 - E t(s t+1)}{r t+1 - E t(r t+1)}] from equations (5) an (13) yiels: λ cov = ( c e c) ( 1 ) σ + λ( φ 1) σ ε. (15) 1 λ Substituting the efinition of f into equation (15), an solving for cov gives the rational expectations equilibrium values for cov an f: λ( 1 c ) + λη( 1 λc) 1 c + η cov = e c c + + < 1 λ 1 η( 1 λ) σ λ( 1 c ) + λη( 1 λc) 1 φ = 0. 1 λc 1 c + η( 1+ λ) > 0, (16) In the rational expectations equilibrium, cov is negative, an f is positive. This implies that the inirect risk premium effect is positive as shown in the previous section. The main issue for the purpose of this paper is whether f is greater or less than one. In orer to etermine this, we will investigate the sign of: ( 1 c ){ λ( 1+ c) 1} η( 1 λc) φ 1 =. ( 1 λc){ 1 c + η( 1+ λ)} (17) Equation (17) shows that f can be either greater or less than one, epening on parameter values. One interesting case arises when the investor is close to being risk neutral. For a very small k, an approximate formula for equation (17) with 1 is: ( 1+ cc ) η φ 1 =. 1 c + η (18) We investigate the conitions require to exhibit the forwar premium anomaly uner low egrees of risk aversion. The forwar premium regression for a short-term interest rate ifferential is st+ 1 st = α + β( rt rt*) + error term. Let ˆβ be the estimate of b. The probability limit of the estimator is: rt rt st st rt st st plim ˆ cov( *, + 1 ) cov(, + 1 ) β =. var( r r*) var( rt ) t t

10 EXCHANGE RATES AND THE TERM STRUCTURE OF INTEREST RATES 83 For this to be negative, we nee cov(r t, s t+1 - s t) < 0, which implies: cov(, rt st+ 1) < cov(, rt st) (19) 1< ( φ 1) η However, substituting equation (18) into (19) oes not prouce a positive value of h that satisfies equation (19). Thus, the population limit of ˆβ is always positive in this moel. The persistent shock creates a positive slope coefficient because both shortan long-term interest rates move together in response to this shock in the moel. The persistent shock ominates the temporary shock in the limit; however, given that the temporary shock can cause the slope to be negative ue to the ominant inirect risk premium effect, there is likely to be a small sample bias when the exchange rate is persistent. We conuct a Monte-Carlo simulation 6 uner these parameterizations to investigate the possibility of the small sample bias. Because the moel is highly stylize so that we can analytically solve for the rational expectation of the covariance, we o not try to calibrate the ata in this paper. 7 Suppose that the AR(1) coefficient of the persistent interest rate shock, c, in equation (7) is close to one (for example, c = 0.9). Then, f in equation (18) becomes greater than one as long as h < When the investor is close to being risk-neutral, the egree of substitution between short- an long-term bons must be high, an consequently, h shoul be very small. Uner these parameter configurations, our moel presente in the previous section preicts that when the measure of the relative magnitue of the inirect risk premium effect, f, is greater than one, the eman from foreign bons increases as the short-term interest rate rises, resulting in the epreciation of omestic currency to cause an expecte future appreciation of omestic currency. A Monte-Carlo simulation base on these parameter configurations consistently generates a negative slope coefficient to show the forwar premium anomaly. As Table 1 shows, the stronger the inirect risk premium effect, the more statistically significant the negative slope coefficient. Table 1. A Monte Carlo Simulation of the Slope Coefficient for the Short-Term Regression (a) ( st+ 1 st) = α + β( rt rt*) + error term H 0 : b = 0 f (h = 0.7) (h = 0.3) (h = 0.) (h = 0.1) (h = 0.1) p lim ˆβ Mean of cov ˆ (b) (, rt st+ 1 st) Mean of ˆβ Negative frequency (c) % significance level () (10% significance level) () (3.4) (14.7) (7.4) (60.7) (96.5) Notes: (a) Sample size is 10 an c = 0.9. (b) Sample covariance. (c) Percentage of negative coefficients among total iteration (1,000). () Percentage of total iteration (1,000) that reject H 0 at a 5% significance level. Numbers in parentheses are that of 10% significance level.

12 EXCHANGE RATES AND THE TERM STRUCTURE OF INTEREST RATES 85 the G-7 countries with cointegrating regressions of real exchange rates onto both short- an long-term interest rate ifferentials. Ogaki an Santaella (000) obtain similar results for Mexico. If the inirect risk premium effect is quantitatively significant, then the effectiveness of central bank attempts to affect the exchange rate by controlling the short-term interest rate epens on whether the long-term interest rate respons to changes in the short-term interest rate. Anecotal evience suggests that further empirical investigation is warrante. For example, from the mile of March 198 to the en of November 198, the Bank of Japan aopte a policy of increasing the omestic shortterm interest rate in orer to cause an appreciation of the yen (Komiya an Sua, 1983, p ). The short-term interest rate in Japan increase, but the yen tene to epreciate rather than appreciate against the US ollar uring this perio. One remarkable fact was that the long-term interest rate i not increase when the Bank of Japan began to increase the short-term interest rate (Komiya an Sua, 1983, p. 349). In typical VAR with the recursive ientification assumption, the elaye overshooting puzzle has been foun as for example in Eichenbaum an Evans (1995). One aspect of the elaye overshooting puzzle is that UIP is severely violate. Therefore, the inirect risk premium effect in principle can help in resolving the puzzle. Incorporating the inirect risk premium effect into an open economy general equilibrium moel is of interest to see whether or not the elaye overshooting arises in such a moel. In this paper, we evelop a highly stylize partial equilibrium moel to obtain the rational expectation of the covariance between the exchange rate an the short-term interest rate, which is a key parameter for the inirect risk premium effect. It is of interest to stuy whether the qualitative implications of the moel still hol in more realistic moels. There has been relatively little empirical work on the interaction between exchange rate an the term structure of interest rates. Further empirical investigation is warrante on this complicate interaction. References Alexius, A., Uncovere Interest Parity Revisite, Review of International Economics 9 (001): Alvarez, F., A. Atkeson, an P.J. Kehoe, Money, Interest Rates, an Exchange Rates with Enogenously Segmente Markets, The Journal of Political Economy 110 (00): Bacchetta, P. an E. Wincoop, Infrequent Portfolio Decisions: A Solution to the Forwar Discount Puzzle, American Economic Review 100 (010): Baillie, R. an T. Bollerslev, The Forwar Premium Anomaly Is Not As Ba As You Think, Journal of International Money an Finance 19 (000): Baillie, R. an R. Kilic, Do asymmetric an Nonlinear Ajustments Explain the Forwar Premium Anomaly? Journal of International Money an Finance 5 (006): 47. Baxter, M., Real Exchange Rates an Real Interest Differentials: Have We Misse the Business-Cycle Relationship? Journal of Monetary Economics 33 (1994):5 37. Blanchar, O. an M. K. Plantes, A Note on Gross Substitutability of Financial Assets, Econometrica 45 (1977): Byeon, Y. an M. Ogaki, An Empirical Investigation of Exchange Rates an the Term Structure of Interest Rates, Working Paper 0, Ohio State University (1999). Chinn, M.D., The (Partial) Rehabilitation of Interest Rate Parity in the Floating Rate Era: Longer Horizons, Alternative Expectations, an Emerging Markets, Journal of International Money an Finance 5 (006):7 1.

13 86 Hyoung-Seok Lim an Masao Ogaki Chinn, M.D. an G. Mereith, Monetary Policy an Long-Horizon Uncovere Interest Parity, IMF Staff Papers, 51 (004). Chinn. M. D. an G. Mereith, Testing Uncovere Interest Parity at Short an Long Horizons uring the Post-Bretton Woos Era, NBER Working Paper 11077, Cambrige, MA: National Bureau of Economic Research (005). Driskill, A.R. an S. McCafferty, Speculation, Rational Expectations, an Stability of the Foreign Exchange Market, Journal of International Economics 10 (1980):9 10. Eichenbaum, M. an C.L. Evans, Some Empirical Evience on the Effects of Shocks to Monetary Policy on Exchange Rates, Quarterly Journal of Economics 110 (1995): Ellingsen, T. an U. Söerström, Monetary Policy an Market Interest Rates, American Economic Review 91 (001): Engel, C., The Forwar Discount Anomaly an the Risk Premium: A Survey of Recent Evience, Journal of Empirical Finance 3 (1996):13 9. Fama, E., Forwar an Spot Exchange Rates, Journal of Monetary Economics 14 (1984): Fisher, E., The Forwar Premium in a Moel with Heterogeneous Prior Beliefs, Journal of International Money an Finance 5 (006): Kobayashi, T., On the Relationship Between Short- an Long-term Interest Rates, International Finance 7 (004): Komiya, R. an M. Sua, Genai Kokusai Kinyuron: Rekishi-Seisaku Hen, Tokyo: Nihon Keizai Shinbun (1983). Maynar, A. an P. Phillips, Rethinking an Ol Empirical Puzzle: Econometric Evience on the Forwar Discount Anomaly, Journal of Applie Econometrics 16 (001): Mark, N. an Y. Wu, Rethinking Deviations from Uncovere Interest Parity: The Role of Covariance Risk an Noise, Economic Journal 108 (1998): McCallum, B., A Reconsieration of the Uncovere Interest Parity Relationship, Journal of Monetary Economics 33 (1994): Meese, R. an K. Rogoff, Was it Real? The Exchange Rate-Interest Rate Differential Relation Over the Moern Floating-Rate Perio, Journal of Finance 43 (1988): Ogaki, M., A Theory of Exchange Rates an the Term Structure of Interest Rates, Working Paper 19, Ohio State University (1999). Ogaki, M., The Inirect An Direct Substitution Effects, American Economic Review 80 (1990): Ogaki, M. an J. A. Santaella, The Exchange Rate an the Term Structure of Interest Rates in Mexico, Journal of Development Economics 63 (000): Royama, S. an K. Hamaa, Substitution an Complementarity in the Choice of Risky Assets, in Hester, D.D. an J. Tobin (es), Risk Aversion an Portfolio Choice, New York: John Wiley (1967). Wu, S., Interest Rate Risk an the Forwar Premium Anomaly in Foreign Exchange Markets, Journal of Money, Creit an Banking 39 (005):43 4. Notes 1. The concepts of irect an inirect risk premium effects are closely relate, but iffer from irect an inirect substitution effects efine by Ogaki (1990).. See Ogaki (1999), an earlier version of the present paper, for etails. 3. Whether v t an u t are inepenent with each other epens on the monetary policy regime as the central bank may change the interest rate in response to a trae shock. An example of a monetary policy regime in which these two shocks are inepenent is a forwar-looking type of Taylor rule responing to both expecte inflation an omestic expecte output gap. 4. Ellingsen an Söerström (001) suggest that the co-movement of term structure of interest rates epens on market participants interpretation of the policy move. They show that if a change in short-term rate is regare as being cause by an unexpecte shift in policy preference, the feeral funs rate an the long term interest rates will move in opposite irections.

14 EXCHANGE RATES AND THE TERM STRUCTURE OF INTEREST RATES 87 Further, Kobayashi (004) emphasizes that the simultaneous occurrence of economic shocks which have ifferent signs an urations can break own the co-movement of term structure of interest rates. 5. Due to the page constraint, we o not report these results here. However, the results are available on request. 6. Gauss for Winows SP Version was use to conuct the simulation for this paper. 7. Baillie an Kilic (006) employ the logistic smooth transition ynamic regression (LSTR) moel to investigate some nonlinear an asymmetric aspects of the relationship between the exchange rate an the short-term interest rate ifferential. They show that the stylize facts of the forwar premium anomaly can be obtaine from calibrating a ata generating process from the estimate LSTR moel as long as transaction costs from closing arbitrage conitions in financial market are large relative to potential gains.

### An intertemporal model of the real exchange rate, stock market, and international debt dynamics: policy simulations

This page may be remove to conceal the ientities of the authors An intertemporal moel of the real exchange rate, stock market, an international ebt ynamics: policy simulations Saziye Gazioglu an W. Davi

### Hull, Chapter 11 + Sections 17.1 and 17.2 Additional reference: John Cox and Mark Rubinstein, Options Markets, Chapter 5

Binomial Moel Hull, Chapter 11 + ections 17.1 an 17.2 Aitional reference: John Cox an Mark Rubinstein, Options Markets, Chapter 5 1. One-Perio Binomial Moel Creating synthetic options (replicating options)

### CURRENCY OPTION PRICING II

Jones Grauate School Rice University Masa Watanabe INTERNATIONAL FINANCE MGMT 657 Calibrating the Binomial Tree to Volatility Black-Scholes Moel for Currency Options Properties of the BS Moel Option Sensitivity

### Risk Management for Derivatives

Risk Management or Derivatives he Greeks are coming the Greeks are coming! Managing risk is important to a large number o iniviuals an institutions he most unamental aspect o business is a process where

### JON HOLTAN. if P&C Insurance Ltd., Oslo, Norway ABSTRACT

OPTIMAL INSURANCE COVERAGE UNDER BONUS-MALUS CONTRACTS BY JON HOLTAN if P&C Insurance Lt., Oslo, Norway ABSTRACT The paper analyses the questions: Shoul or shoul not an iniviual buy insurance? An if so,

### The one-year non-life insurance risk

The one-year non-life insurance risk Ohlsson, Esbjörn & Lauzeningks, Jan Abstract With few exceptions, the literature on non-life insurance reserve risk has been evote to the ultimo risk, the risk in the

### Professional Level Options Module, Paper P4(SGP)

Answers Professional Level Options Moule, Paper P4(SGP) Avance Financial Management (Singapore) December 2007 Answers Tutorial note: These moel answers are consierably longer an more etaile than woul be

### Optimal Energy Commitments with Storage and Intermittent Supply

Submitte to Operations Research manuscript OPRE-2009-09-406 Optimal Energy Commitments with Storage an Intermittent Supply Jae Ho Kim Department of Electrical Engineering, Princeton University, Princeton,

### State of Louisiana Office of Information Technology. Change Management Plan

State of Louisiana Office of Information Technology Change Management Plan Table of Contents Change Management Overview Change Management Plan Key Consierations Organizational Transition Stages Change

### Ch 10. Arithmetic Average Options and Asian Opitons

Ch 10. Arithmetic Average Options an Asian Opitons I. Asian Option an the Analytic Pricing Formula II. Binomial Tree Moel to Price Average Options III. Combination of Arithmetic Average an Reset Options

### Detecting Possibly Fraudulent or Error-Prone Survey Data Using Benford s Law

Detecting Possibly Frauulent or Error-Prone Survey Data Using Benfor s Law Davi Swanson, Moon Jung Cho, John Eltinge U.S. Bureau of Labor Statistics 2 Massachusetts Ave., NE, Room 3650, Washington, DC

### Random Walk Expectations and the Forward Discount Puzzle

Random Walk Expectations and the Forward Discount Puzzle Philippe Bacchetta and Eric van Wincoop* Two well-known, but seemingly contradictory, features of exchange rates are that they are close to a random

### Chapter 4: Elasticity

Chapter : Elasticity Elasticity of eman: It measures the responsiveness of quantity emane (or eman) with respect to changes in its own price (or income or the price of some other commoity). Why is Elasticity

### CHAPTER 5 : CALCULUS

Dr Roger Ni (Queen Mary, University of Lonon) - 5. CHAPTER 5 : CALCULUS Differentiation Introuction to Differentiation Calculus is a branch of mathematics which concerns itself with change. Irrespective

### Consumer Referrals. Maria Arbatskaya and Hideo Konishi. October 28, 2014

Consumer Referrals Maria Arbatskaya an Hieo Konishi October 28, 2014 Abstract In many inustries, rms rewar their customers for making referrals. We analyze the optimal policy mix of price, avertising intensity,

### Optimal Control Policy of a Production and Inventory System for multi-product in Segmented Market

RATIO MATHEMATICA 25 (2013), 29 46 ISSN:1592-7415 Optimal Control Policy of a Prouction an Inventory System for multi-prouct in Segmente Market Kuleep Chauhary, Yogener Singh, P. C. Jha Department of Operational

### Answers to the Practice Problems for Test 2

Answers to the Practice Problems for Test 2 Davi Murphy. Fin f (x) if it is known that x [f(2x)] = x2. By the chain rule, x [f(2x)] = f (2x) 2, so 2f (2x) = x 2. Hence f (2x) = x 2 /2, but the lefthan

### Digital barrier option contract with exponential random time

IMA Journal of Applie Mathematics Avance Access publishe June 9, IMA Journal of Applie Mathematics ) Page of 9 oi:.93/imamat/hxs3 Digital barrier option contract with exponential ranom time Doobae Jun

### Math 230.01, Fall 2012: HW 1 Solutions

Math 3., Fall : HW Solutions Problem (p.9 #). Suppose a wor is picke at ranom from this sentence. Fin: a) the chance the wor has at least letters; SOLUTION: All wors are equally likely to be chosen. The

### The VAR models discussed so fare are appropriate for modeling I(0) data, like asset returns or growth rates of macroeconomic time series.

Cointegration The VAR models discussed so fare are appropriate for modeling I(0) data, like asset returns or growth rates of macroeconomic time series. Economic theory, however, often implies equilibrium

### Mathematics Review for Economists

Mathematics Review for Economists by John E. Floy University of Toronto May 9, 2013 This ocument presents a review of very basic mathematics for use by stuents who plan to stuy economics in grauate school

### The relationship between exchange rates, interest rates. In this lecture we will learn how exchange rates accommodate equilibrium in

The relationship between exchange rates, interest rates In this lecture we will learn how exchange rates accommodate equilibrium in financial markets. For this purpose we examine the relationship between

### Enterprise Resource Planning

Enterprise Resource Planning MPC 6 th Eition Chapter 1a McGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserve. Enterprise Resource Planning A comprehensive software approach

### Mandate-Based Health Reform and the Labor Market: Evidence from the Massachusetts Reform

Manate-Base Health Reform an the Labor Market: Evience from the Massachusetts Reform Jonathan T. Kolsta Wharton School, University of Pennsylvania an NBER Amana E. Kowalski Department of Economics, Yale

### Liquidity and Corporate Debt Market Timing

Liquiity an Corporate Debt Market Timing Marina Balboa Faculty of Economics University of Alicante Phone: +34 965903621 Fax: +34 965903621 marina.balboa@ua.es Belén Nieto (Corresponing author) Faculty

### New Trade Models, New Welfare Implications

New Trae Moels, New Welfare Implications Marc J. Melitz Harvar University, NBER an CEPR Stephen J. Reing Princeton University, NBER an CEPR August 13, 2014 Abstract We show that enogenous firm selection

### MSc. Econ: MATHEMATICAL STATISTICS, 1995 MAXIMUM-LIKELIHOOD ESTIMATION

MAXIMUM-LIKELIHOOD ESTIMATION The General Theory of M-L Estimation In orer to erive an M-L estimator, we are boun to make an assumption about the functional form of the istribution which generates the

### Option Pricing for Inventory Management and Control

Option Pricing for Inventory Management an Control Bryant Angelos, McKay Heasley, an Jeffrey Humpherys Abstract We explore the use of option contracts as a means of managing an controlling inventories

### Net Neutrality, Network Capacity, and Innovation at the Edges

Net Neutrality, Network Capacity, an Innovation at the Eges Jay Pil Choi Doh-Shin Jeon Byung-Cheol Kim May 22, 2015 Abstract We stuy how net neutrality regulations affect a high-banwith content provier(cp)

### Sensitivity Analysis of Non-linear Performance with Probability Distortion

Preprints of the 19th Worl Congress The International Feeration of Automatic Control Cape Town, South Africa. August 24-29, 214 Sensitivity Analysis of Non-linear Performance with Probability Distortion

### SEC Issues Proposed Guidance to Fund Boards Relating to Best Execution and Soft Dollars

September 2008 / Issue 21 A legal upate from Dechert s Financial Services Group SEC Issues Propose Guiance to Fun Boars Relating to Best Execution an Soft Dollars The Securities an Exchange Commission

### MODELLING OF TWO STRATEGIES IN INVENTORY CONTROL SYSTEM WITH RANDOM LEAD TIME AND DEMAND

art I. robobabilystic Moels Computer Moelling an New echnologies 27 Vol. No. 2-3 ransport an elecommunication Institute omonosova iga V-9 atvia MOEING OF WO AEGIE IN INVENOY CONO YEM WIH ANOM EA IME AN

### The Inefficiency of Marginal cost pricing on roads

The Inefficiency of Marginal cost pricing on roas Sofia Grahn-Voornevel Sweish National Roa an Transport Research Institute VTI CTS Working Paper 4:6 stract The economic principle of roa pricing is that

### Optimal Control Of Production Inventory Systems With Deteriorating Items And Dynamic Costs

Applie Mathematics E-Notes, 8(2008), 194-202 c ISSN 1607-2510 Available free at mirror sites of http://www.math.nthu.eu.tw/ amen/ Optimal Control Of Prouction Inventory Systems With Deteriorating Items

### UCLA STAT 13 Introduction to Statistical Methods for the Life and Health Sciences. Chapter 9 Paired Data. Paired data. Paired data

UCLA STAT 3 Introuction to Statistical Methos for the Life an Health Sciences Instructor: Ivo Dinov, Asst. Prof. of Statistics an Neurology Chapter 9 Paire Data Teaching Assistants: Jacquelina Dacosta

### Web Appendices to Selling to Overcon dent Consumers

Web Appenices to Selling to Overcon ent Consumers Michael D. Grubb MIT Sloan School of Management Cambrige, MA 02142 mgrubbmit.eu www.mit.eu/~mgrubb May 2, 2008 B Option Pricing Intuition This appenix

### Exchange rates and long-term bonds

Exchange rates and long-term bonds Annika Alexius and Peter Sellin April 2002 Abstract Tentative evidence suggests that the empirical failure of uncovered interest parity (UIP) is confined to short-term

### Data Center Power System Reliability Beyond the 9 s: A Practical Approach

Data Center Power System Reliability Beyon the 9 s: A Practical Approach Bill Brown, P.E., Square D Critical Power Competency Center. Abstract Reliability has always been the focus of mission-critical

### MASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.436J/15.085J Fall 2008 Lecture 14 10/27/2008 MOMENT GENERATING FUNCTIONS

MASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.436J/15.085J Fall 2008 Lecture 14 10/27/2008 MOMENT GENERATING FUNCTIONS Contents 1. Moment generating functions 2. Sum of a ranom number of ranom variables 3. Transforms

### APPLICATION OF CALCULUS IN COMMERCE AND ECONOMICS

Application of Calculus in Commerce an Economics 41 APPLICATION OF CALCULUS IN COMMERCE AND ECONOMICS æ We have learnt in calculus that when 'y' is a function of '', the erivative of y w.r.to i.e. y ö

### 15.2. First-Order Linear Differential Equations. First-Order Linear Differential Equations Bernoulli Equations Applications

00 CHAPTER 5 Differential Equations SECTION 5. First-Orer Linear Differential Equations First-Orer Linear Differential Equations Bernoulli Equations Applications First-Orer Linear Differential Equations

### Product Differentiation for Software-as-a-Service Providers

University of Augsburg Prof. Dr. Hans Ulrich Buhl Research Center Finance & Information Management Department of Information Systems Engineering & Financial Management Discussion Paper WI-99 Prouct Differentiation

### Web Appendices of Selling to Overcon dent Consumers

Web Appenices of Selling to Overcon ent Consumers Michael D. Grubb A Option Pricing Intuition This appenix provies aitional intuition base on option pricing for the result in Proposition 2. Consier the

### Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices

THE JOURNAL OF FINANCE VOL LIII, NO. 2 APRIL 1998 Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices YACINE AÏT-SAHALIA an ANDREW W. LO* ABSTRACT Implicit in the prices

### On the Efficiency of Competitive Stock Markets Where Traders Have Diverse Information

Finance 400 A. Penati - G. Pennacchi Notes on On the Efficiency of Competitive Stock Markets Where Traders Have Diverse Information by Sanford Grossman This model shows how the heterogeneous information

### 10.2 Systems of Linear Equations: Matrices

SECTION 0.2 Systems of Linear Equations: Matrices 7 0.2 Systems of Linear Equations: Matrices OBJECTIVES Write the Augmente Matrix of a System of Linear Equations 2 Write the System from the Augmente Matrix

### Optimizing Multiple Stock Trading Rules using Genetic Algorithms

Optimizing Multiple Stock Traing Rules using Genetic Algorithms Ariano Simões, Rui Neves, Nuno Horta Instituto as Telecomunicações, Instituto Superior Técnico Av. Rovisco Pais, 040-00 Lisboa, Portugal.

### INFLATION, INTEREST RATE, AND EXCHANGE RATE: WHAT IS THE RELATIONSHIP?

107 INFLATION, INTEREST RATE, AND EXCHANGE RATE: WHAT IS THE RELATIONSHIP? Maurice K. Shalishali, Columbus State University Johnny C. Ho, Columbus State University ABSTRACT A test of IFE (International

### CALCULATION INSTRUCTIONS

Energy Saving Guarantee Contract ppenix 8 CLCULTION INSTRUCTIONS Calculation Instructions for the Determination of the Energy Costs aseline, the nnual mounts of Savings an the Remuneration 1 asics ll prices

### Investing in Foreign Currency is like Betting on your Intertemporal Marginal Rate of Substitution.

Investing in Foreign Currency is like Betting on your Intertemporal Marginal Rate of Substitution. Hanno Lustig UCLA and NBER Adrien Verdelhan Boston University December 13, 2005 Abstract Investors earn

### Wage Compression, Employment Restrictions, and Unemployment: The Case of Mauritius

WP/04/205 Wage Compression, Employment Restrictions, an Unemployment: The Case of Mauritius Nathan Porter 2004 International Monetary Fun WP/04/205 IMF Working Paper Finance Department Wage Compression,

### Lecture 1: Asset pricing and the equity premium puzzle

Lecture 1: Asset pricing and the equity premium puzzle Simon Gilchrist Boston Univerity and NBER EC 745 Fall, 2013 Overview Some basic facts. Study the asset pricing implications of household portfolio

### Stock Market Value Prediction Using Neural Networks

Stock Market Value Preiction Using Neural Networks Mahi Pakaman Naeini IT & Computer Engineering Department Islamic Aza University Paran Branch e-mail: m.pakaman@ece.ut.ac.ir Hamireza Taremian Engineering

Cbons.Ru Lt. irogovskaya nab., 21, St. etersburg hone: +7 (812) 336-97-21 http://www.cbons-group.com Bon Calculator Bon calculator is esigne to calculate analytical parameters use in assessment of bons.

### Debt cycles, instability and fiscal rules: a Godley-Minsky model

Faculty of usiness an Law Debt cycles, instability an fiscal rules: a Goley-Minsky moel Yannis Dafermos Department of Accounting, Economics an Finance, University of the West of Englan, ristol, UK Yannis.Dafermos@uwe.ac.uk

### A Generalization of Sauer s Lemma to Classes of Large-Margin Functions

A Generalization of Sauer s Lemma to Classes of Large-Margin Functions Joel Ratsaby University College Lonon Gower Street, Lonon WC1E 6BT, Unite Kingom J.Ratsaby@cs.ucl.ac.uk, WWW home page: http://www.cs.ucl.ac.uk/staff/j.ratsaby/

### Purpose of the Experiments. Principles and Error Analysis. ε 0 is the dielectric constant,ε 0. ε r. = 8.854 10 12 F/m is the permittivity of

Experiments with Parallel Plate Capacitors to Evaluate the Capacitance Calculation an Gauss Law in Electricity, an to Measure the Dielectric Constants of a Few Soli an Liqui Samples Table of Contents Purpose

### Lecture L25-3D Rigid Body Kinematics

J. Peraire, S. Winall 16.07 Dynamics Fall 2008 Version 2.0 Lecture L25-3D Rigi Boy Kinematics In this lecture, we consier the motion of a 3D rigi boy. We shall see that in the general three-imensional

### Modelling and Resolving Software Dependencies

June 15, 2005 Abstract Many Linux istributions an other moern operating systems feature the explicit eclaration of (often complex) epenency relationships between the pieces of software

### Exponential Functions: Differentiation and Integration. The Natural Exponential Function

46_54.q //4 :59 PM Page 5 5 CHAPTER 5 Logarithmic, Eponential, an Other Transcenental Functions Section 5.4 f () = e f() = ln The inverse function of the natural logarithmic function is the natural eponential

### Section 3.3. Differentiation of Polynomials and Rational Functions. Difference Equations to Differential Equations

Difference Equations to Differential Equations Section 3.3 Differentiation of Polynomials an Rational Functions In tis section we begin te task of iscovering rules for ifferentiating various classes of

### Asymmetric Neutrality Regulation and Innovation at the Edges: Fixed vs. Mobile Networks

TSE 521 August 2014 Asymmetric Neutrality Regulation an Innovation at the Eges: Fixe vs. Mobile Networks Jay Pil Choi, Doh Shin Jeon an Byung Cheol Kim Asymmetric Neutrality Regulation an Innovation at

### Study on the Price Elasticity of Demand of Beijing Subway

Journal of Traffic an Logistics Engineering, Vol, 1, No. 1 June 2013 Stuy on the Price Elasticity of Deman of Beijing Subway Yanan Miao an Liang Gao MOE Key Laboratory for Urban Transportation Complex

### GRADO EN ECONOMÍA. Is the Forward Rate a True Unbiased Predictor of the Future Spot Exchange Rate?

FACULTAD DE CIENCIAS ECONÓMICAS Y EMPRESARIALES GRADO EN ECONOMÍA Is the Forward Rate a True Unbiased Predictor of the Future Spot Exchange Rate? Autor: Elena Renedo Sánchez Tutor: Juan Ángel Jiménez Martín

### Differentiability of Exponential Functions

Differentiability of Exponential Functions Philip M. Anselone an John W. Lee Philip Anselone (panselone@actionnet.net) receive his Ph.D. from Oregon State in 1957. After a few years at Johns Hopkins an

### Search Advertising Based Promotion Strategies for Online Retailers

Search Avertising Base Promotion Strategies for Online Retailers Amit Mehra The Inian School of Business yeraba, Inia Amit Mehra@isb.eu ABSTRACT Web site aresses of small on line retailers are often unknown

### Safety Stock or Excess Capacity: Trade-offs under Supply Risk

Safety Stock or Excess Capacity: Trae-offs uner Supply Risk Aahaar Chaturvei Victor Martínez-e-Albéniz IESE Business School, University of Navarra Av. Pearson, 08034 Barcelona, Spain achaturvei@iese.eu

### On Adaboost and Optimal Betting Strategies

On Aaboost an Optimal Betting Strategies Pasquale Malacaria 1 an Fabrizio Smerali 1 1 School of Electronic Engineering an Computer Science, Queen Mary University of Lonon, Lonon, UK Abstract We explore

### Liquid Pricing for Digital Infrastructure Services

iqui Pricing for Digital Infrastructure Services Subhajyoti Banyopahyay * an sing Kenneth Cheng Department of Decision an Information Sciences Warrington College of Business Aministration University of

### Chapter 9 AIRPORT SYSTEM PLANNING

Chapter 9 AIRPORT SYSTEM PLANNING. Photo creit Dorn McGrath, Jr Contents Page The Planning Process................................................... 189 Airport Master Planning..............................................

### A New Pricing Model for Competitive Telecommunications Services Using Congestion Discounts

A New Pricing Moel for Competitive Telecommunications Services Using Congestion Discounts N. Keon an G. Ananalingam Department of Systems Engineering University of Pennsylvania Philaelphia, PA 19104-6315

### Modeling and Predicting Popularity Dynamics via Reinforced Poisson Processes

Proceeings of the Twenty-Eighth AAAI Conference on Artificial Intelligence Moeling an Preicting Popularity Dynamics via Reinforce Poisson Processes Huawei Shen 1, Dashun Wang 2, Chaoming Song 3, Albert-László

### ISSN: 2277-3754 ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 3, Issue 12, June 2014

ISSN: 77-754 ISO 900:008 Certifie International Journal of Engineering an Innovative echnology (IJEI) Volume, Issue, June 04 Manufacturing process with isruption uner Quaratic Deman for Deteriorating Inventory

### INFLUENCE OF GPS TECHNOLOGY ON COST CONTROL AND MAINTENANCE OF VEHICLES

1 st Logistics International Conference Belgrae, Serbia 28-30 November 2013 INFLUENCE OF GPS TECHNOLOGY ON COST CONTROL AND MAINTENANCE OF VEHICLES Goran N. Raoičić * University of Niš, Faculty of Mechanical

### A Case Study of Applying SOM in Market Segmentation of Automobile Insurance Customers

International Journal of Database Theory an Application, pp.25-36 http://x.oi.org/10.14257/ijta.2014.7.1.03 A Case Stuy of Applying SOM in Market Segmentation of Automobile Insurance Customers Vahi Golmah

### A Data Placement Strategy in Scientific Cloud Workflows

A Data Placement Strategy in Scientific Clou Workflows Dong Yuan, Yun Yang, Xiao Liu, Jinjun Chen Faculty of Information an Communication Technologies, Swinburne University of Technology Hawthorn, Melbourne,

### Is the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate?

Is the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate? Emily Polito, Trinity College In the past two decades, there have been many empirical studies both in support of and opposing

### Improving Direct Marketing Profitability with Neural Networks

Volume 9 o.5, September 011 Improving Direct Marketing Profitability with eural etworks Zaiyong Tang Salem State University Salem, MA 01970 ABSTRACT Data mining in irect marketing aims at ientifying the

### Factor Prices and International Trade: A Unifying Perspective

Factor Prices an International Trae: A Unifying Perspective Ariel Burstein UCLA an NBER Jonathan Vogel Columbia an NBER October 20 Abstract How o trae liberalizations a ect relative factor prices an to

### Lagrangian and Hamiltonian Mechanics

Lagrangian an Hamiltonian Mechanics D.G. Simpson, Ph.D. Department of Physical Sciences an Engineering Prince George s Community College December 5, 007 Introuction In this course we have been stuying

### The most common model to support workforce management of telephone call centers is

Designing a Call Center with Impatient Customers O. Garnett A. Manelbaum M. Reiman Davison Faculty of Inustrial Engineering an Management, Technion, Haifa 32000, Israel Davison Faculty of Inustrial Engineering

### Cross-Over Analysis Using T-Tests

Chapter 35 Cross-Over Analysis Using -ests Introuction his proceure analyzes ata from a two-treatment, two-perio (x) cross-over esign. he response is assume to be a continuous ranom variable that follows

### 5 Isotope effects on vibrational relaxation and hydrogen-bond dynamics in water

5 Isotope effects on vibrational relaxation an hyrogen-bon ynamics in water Pump probe experiments HDO issolve in liqui H O show the spectral ynamics an the vibrational relaxation of the OD stretch vibration.

### Di usion on Social Networks. Current Version: June 6, 2006 Appeared in: Économie Publique, Numéro 16, pp 3-16, 2005/1.

Di usion on Social Networks Matthew O. Jackson y Caltech Leeat Yariv z Caltech Current Version: June 6, 2006 Appeare in: Économie Publique, Numéro 16, pp 3-16, 2005/1. Abstract. We analyze a moel of i

### A New Evaluation Measure for Information Retrieval Systems

A New Evaluation Measure for Information Retrieval Systems Martin Mehlitz martin.mehlitz@ai-labor.e Christian Bauckhage Deutsche Telekom Laboratories christian.bauckhage@telekom.e Jérôme Kunegis jerome.kunegis@ai-labor.e

### The influence of anti-viral drug therapy on the evolution of HIV-1 pathogens

DIMACS Series in Discrete Mathematics an Theoretical Computer Science Volume 7, 26 The influence of anti-viral rug therapy on the evolution of HIV- pathogens Zhilan Feng an Libin Rong Abstract. An age-structure

### Risk Adjustment for Poker Players

Risk Ajustment for Poker Players William Chin DePaul University, Chicago, Illinois Marc Ingenoso Conger Asset Management LLC, Chicago, Illinois September, 2006 Introuction In this article we consier risk

### Here the units used are radians and sin x = sin(x radians). Recall that sin x and cos x are defined and continuous everywhere and

Lecture 9 : Derivatives of Trigonometric Functions (Please review Trigonometry uner Algebra/Precalculus Review on the class webpage.) In this section we will look at the erivatives of the trigonometric

### Modules 6 and 7: Markets, Prices, Supply, and Demand practice problems. Practice problems and illustrative test questions for the final exam

Moules 6 an 7: Markets, Prices, Supply, an Deman practice problems Practice problems an illustrative test questions for the final exam (The attache PDF file has better formatting.) This posting gives sample

### On the long run relationship between gold and silver prices A note

Global Finance Journal 12 (2001) 299 303 On the long run relationship between gold and silver prices A note C. Ciner* Northeastern University College of Business Administration, Boston, MA 02115-5000,

### A Comparison of Performance Measures for Online Algorithms

A Comparison of Performance Measures for Online Algorithms Joan Boyar 1, Sany Irani 2, an Kim S. Larsen 1 1 Department of Mathematics an Computer Science, University of Southern Denmark, Campusvej 55,

### Cost Efficient Datacenter Selection for Cloud Services

Cost Efficient Datacenter Selection for Clou Services Hong u, Baochun Li henryxu, bli@eecg.toronto.eu Department of Electrical an Computer Engineering University of Toronto Abstract Many clou services

### Form 63-29A Ocean Marine Profits Tax Return

Form 63-29A Ocean Marine Profits Tax Return 2001 Massachusetts Department of Revenue To be file by omestic an foreign insurance companies which are subject to the provisions of Massachusetts General Laws,

### There are two different ways you can interpret the information given in a demand curve.

Econ 500 Microeconomic Review Deman What these notes hope to o is to o a quick review of supply, eman, an equilibrium, with an emphasis on a more quantifiable approach. Deman Curve (Big icture) The whole

### Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence

Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence Zeldes, QJE 1989 Background (Not in Paper) Income Uncertainty dates back to even earlier years, with the seminal work of

### 4. Important theorems in quantum mechanics

TFY4215 Kjemisk fysikk og kvantemekanikk - Tillegg 4 1 TILLEGG 4 4. Important theorems in quantum mechanics Before attacking three-imensional potentials in the next chapter, we shall in chapter 4 of this

### The Quick Calculus Tutorial

The Quick Calculus Tutorial This text is a quick introuction into Calculus ieas an techniques. It is esigne to help you if you take the Calculus base course Physics 211 at the same time with Calculus I,

### The Uncovered Interest Rate Parity Puzzle in the Foreign Exchange Market

The Uncovered Interest Rate Parity Puzzle in the Foreign Exchange Market Sahil Aggarwal * New York University This draft: May 2013 Abstract. This paper focuses on the theory of uncovered interest rate