# From Ruin Theory to Solvency in Non-Life Insurance

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 From Ruin Theory to Solvency in Non-Life Insurance Mario V. Wüthrich RiskLab ETH Zurich & Swiss Finance Institute SFI January 23, 2014 LUH Colloquium Versicherungs- und Finanzmathematik Leibniz Universität Hannover

2 Aim of this presentation We start from Lundberg s thesis (1903) on ruin theory and modify his model step by step until we arrive at today s solvency considerations surplus process 1

3 Cramér-Lundberg model Consider the surplus process (C t ) t 0 given by where L t = N t i=1 c 0 0 π > 0 Y i 0 C t = c 0 + πt N t i=1 initial capital, premium rate, Y i, Harald Cramér homogeneous compound Poisson claims process, satisfying the net profit condition (NPC): π > E[L 1 ]. 2

4 Ultimate ruin probability The ultimate ruin probability for initial capital c 0 0 is given by [ ] [ ] ψ(c 0 ) = P inf C t < 0 t R + C 0 = c 0 = P c0 inf C t < 0, t R + i.e. this is the infinite time horizon ruin probability. 10 Under (NPC): ψ(c 0 ) < 1 for all c surplus process 3

5 Lundberg s exponential bound Assume (NPC) and that the Lundberg coefficient γ > 0 exists. Then, we have exponential bound ψ(c 0 ) exp{ γc 0 }, for all c 0 0 (large deviation principle (LDP)). This is the light-tailed case, i.e. for the existence of γ > 0 we need exponentially decaying survival probabilities of the claim sizes Y i, because we require E[exp{γY i }] <. Filip Lundberg 4

6 Subexponential case Von Bahr, Veraverbeke, Embrechts investigate the heavy-tailed case. In particular, for Y i i.i.d. Pareto(α > 1) and (NPC): ψ(c 0 ) const c α+1 0 as c 0. Heavy-tailed case provides a much slower decay Paul Embrechts gamma surplus process Pareto surplus process 5

7 Discrete time ruin considerations 10 Insurance companies cannot continuously control their surplus processes (C t ) t gamma surplus process They close their books and check their surplus on a yearly time grid. Consider the discrete time ruin probability [ ] [ ] P c0 inf C n < 0 P c0 inf C t < 0 n N 0 t R + = ψ(c 0 ). This leads to the study of the random walk (C n c 0 ) n N0 for (discrete time) accounting years n N 0. 6

8 One-period ruin problem Insured buy one-year nonlife insurance contracts: why bother about ultimate ruin probabilities? gamma surplus process Moreover, initial capital c 0 0 needs to be re-adjusted every accounting year. Consider the (discrete time) one-year ruin probability [ ] [ ] P c0 [C 1 < 0] P c0 inf C n < 0 P c0 inf C t < 0 n N 0 t R + = ψ(c 0 ). This leads to the study of the surplus C 1 = c 0 + π N 1 i=1 Y i at time 1. 7

9 One-period problem and real world considerations Why do we study so complex models when the real world problem is so simple? gamma surplus process Total asset value at time 1: A 1 = c 0 + π. Total liabilities at time 1: L 1 = N 1 i=1 Y i. C 1 = c 0 + π N 1 i=1 Y i = A 1 L 1??? 0. (1) There are many modeling issues hidden in (1)! We discuss them step by step. 8

10 Value-at-Risk (VaR) risk measure C 1 = A 1 L 1??? 0. Value-at-Risk on confidence level p = 99.5% (Solvency II): choose c 0 minimal such that P c0 [C 1 0] = P [A 1 L 1 ] = P [L 1 c 0 π 0] p. Freddy Delbaen Choose other (normalized) risk measures ϱ : M L 1 (Ω, F, P) R and study ϱ(l 1 A 1 ) = ϱ (L 1 c 0 π)??? 0, where implies SOLVENCY w.r.t. risk measure ϱ. 9

11 Asset return and financial risk (1/2) Initial capital at time 0: c 0 0. Premium received at time 0 for accounting year 1: π > 0. Total asset value at time 0: a 0 = c 0 + π > 0. This asset value a 0 is invested in different assets k {1,..., K} at time 0. asset classes cash and cash equivalents debt securities (bonds, loans, mortgages) real estate & property equity, private equity derivatives & hedge funds insurance & reinsurance assets other assets 10

12 Asset return and financial risk (2/2) Choose an asset portfolio x = (x 1,..., x K ) R K at time 0 with initial value a 0 = K k=1 x k S (k) 0, where S (k) t is the price of asset k at time t. This provides value at time 1 A 1 = K k=1 x k S (k) 1 = a 0 (1 + w R 1 ), for buy & hold asset strategy w = w(x) R K and (random) return vector R 1. ϱ(l 1 A 1 ) = ϱ (L 1 a 0 (1 + w R 1 ))??? 0. where implies solvency w.r.t. risk measure ϱ and business plan (L 1, a 0, w). 11

13 Insurance claim (liability) modeling (1/2) MAIN ISSUE: modeling of insurance claim L 1 = N 1 i=1 Y i. Insurance claims are neither known nor can immediately be settled at occurrence! premium π accident date reporting date claims closing insurance period (accounting year 1) claims cash flows X = ( X 1, X 2, ) time Insurance claims of accounting year 1 generate insurance liability cash flow X: X = (X 1, X 2,...) with X t being the payment in accounting year t. Question: How is the cash flow X related to the insurance claim L 1? 12

14 Insurance claim (liability) modeling (2/2) premium π accident date reporting date claims closing insurance period (accounting year 1) claims cash flows X = ( X 1, X 2, ) time Main tasks: cash flow X = (X 1, X 2,...) modeling, cash flow X = (X 1, X 2,...) prediction, cash flow X = (X 1, X 2,...) valuation, using all available relevant information: exactly here the one-period problem turns into a multi-period problem. 13

15 Best-estimate reserves Choose a filtered probability space (Ω, F, P, F) with filtration F = (F t ) t N0 and assume cash flow X is F-adapted. 1st attempt to define L 1 (interpretation of Solvency II): L 1 = X 1 + s 2 P (1, s) E [X s F 1 ], where E [X s F 1 ] is the best-estimate reserve (prediction) of X s at time 1; P (1, s) is the zero-coupon bond price at time 1 for maturity date s. Note that L 1 is F 1 -measurable, i.e. observable w.r.t. F 1 (information at time 1). 14

16 1st attempt to define L 1 L 1 = X 1 + s 2 P (1, s) E [X s F 1 ]. (2) Issue: Solvency II asks for economic balance sheet, but L 1 is not an economic value. (a) Risk margin is missing: any risk-averse risk bearer asks for such a (profit) margin. (b) Zero-coupon bond prices and claims cash flows X s, s 2, may be influenced by the same risk factors and, thus, there is no decoupling such as (2). 15

17 2nd attempt to define L 1 Choose an appropriate state-price deflator ϕ = (ϕ t ) t 1 and L 1 = X 1 + s 2 1 ϕ 1 E [ϕ s X s F 1 ]. ϕ = (ϕ t ) t 1 is a strictly positive, a.s., and F-adapted. ϕ = (ϕ t ) t 1 reflects price formation at financial markets, in particular, P (1, s) = 1 ϕ 1 E [ϕ s F 1 ]. Hans Bühlmann If ϕ s and X s are positively correlated, given F 1, then L 1 X 1 + s 2 P (1, s) E [X s F 1 ]. 16

18 Solvency at time 0 Choose a filtered probability space (Ω, F, P, F) such that it caries the random vectors ϕ (state-price deflator), R 1 (returns of assets) and X (insurance liability cash flows) in a reasonable way. The business plan (X, a 0, w) is solvent w.r.t. the risk measure ϱ and state-price deflator ϕ if ϱ(l 1 A 1 ) = ϱ X 1 + s 2 1 E [ϕ s X s F 1 ] a 0 (1 + w R 1 ) 0. ϕ 1 Thus, it is likely (measured by ϱ and ϕ) that the liabilities L 1 are covered by assets A 1 at time 1 in an economic balance sheet. 17

19 Acceptability arbitrage The choice of the state-price deflator ϕ and the risk measure ϱ cannot be done independently of each other: ϕ describes the risk reward; ϱ describes the risk punishment. Assume there exist acceptable zero-cost portfolios Y with E[ϕ Y] = 0 and ϱ Y 1 + s 2 1 E [ϕ s Y s F 1 ] < 0. ϕ 1 P. Artzner Then, unacceptable positions can be turned into acceptable ones just by loading on more risk = acceptability arbitrage. Reasonable solvency models (ϕ, ϱ) should exclude acceptability arbitrage, see Artzner, Delbaen, Eisele, Koch-Medina. 18

20 Asset & liability management (ALM) The business plan (X, a 0, w) is solvent w.r.t. risk measure ϱ and state-price deflator ϕ if ϱ(l 1 A 1 ) = ϱ X 1 + s 2 1 ( E [ϕ s X s F 1 ] a w ) R 1 0. ϕ 1 ALM optimize this business plan (X, a 0, w): Which asset strategy w R K minimizes the capital a 0 = c 0 + π and we still remain solvent? This is a non-trivial optimization problem. Of course, we need to exclude acceptability arbitrage, which may also provide restrictions on the possible asset strategies w = eligible assets. 19

21 Summary of modeling tasks Provide reasonable stochastic models for R 1, X and ϕ (yield curve extrapolation). What is a reasonable profit margin for risk bearing expressed by ϕ? Which risk measure(s) ϱ should be preferred? ( No-acceptability arbitrage!) Modeling is often split into different risk modules: (financial) market risk insurance risk (underwriting and reserve risks) credit risk operational risk Issue: dependence modeling and aggregation of risk modules. Aggregation over different accounting years and lines of business? 20

22 Dynamic considerations Are we happy with the above considerations? Not entirely! Liability run-off is a multi-period problem: We also want sensible dynamic behavior. This leads to the consideration of multi-period problems and super-martingales. 21

### Runoff of the Claims Reserving Uncertainty in Non-Life Insurance: A Case Study

1 Runoff of the Claims Reserving Uncertainty in Non-Life Insurance: A Case Study Mario V. Wüthrich Abstract: The market-consistent value of insurance liabilities consists of the best-estimate prediction

### Optimal reinsurance with ruin probability target

Optimal reinsurance with ruin probability target Arthur Charpentier 7th International Workshop on Rare Event Simulation, Sept. 2008 http ://blogperso.univ-rennes1.fr/arthur.charpentier/ 1 Ruin, solvency

### Non-Life Insurance Mathematics

Thomas Mikosch Non-Life Insurance Mathematics An Introduction with the Poisson Process Second Edition 4y Springer Contents Part I Collective Risk Models 1 The Basic Model 3 2 Models for the Claim Number

### The Investment Implications of Solvency II

The Investment Implications of Solvency II André van Vliet, Ortec Finance, Insurance Risk Management Anthony Brown, FSA Outline Introduction - Solvency II - Strategic Decision Making Impact of investment

### 1 Introduction. 1.1 Three pillar approach

1 Introduction 1.1 Three pillar approach The recent years have shown that (financial) companies need to have a good management, a good business strategy, a good financial strength and a sound risk management

### Actuarial Risk Management

ARA syllabus Actuarial Risk Management Aim: To provide the technical skills to apply the principles and methodologies studied under actuarial technical subjects for the identification, quantification and

### AXA s approach to Asset Liability Management. HELVEA Insurance Capital Adequacy and Solvency Day April 28th, 2005

AXA s approach to Asset Liability Management HELVEA Insurance Capital Adequacy and Solvency Day April 28th, 2005 ALM in AXA has always been based on a long-term view Even though Solvency II framework is

### Risk Margins and Solvency II Peter England and Richard Millns

Risk Margins and Solvency II Peter England and Richard Millns GIRO conference and exhibition Liverpool, 11-14 October 2011 Agenda Part 1 A quick re-cap from last year (and the year before) Part 2 Further

### How to model Operational Risk?

How to model Operational Risk? Paul Embrechts Director RiskLab, Department of Mathematics, ETH Zurich Member of the ETH Risk Center Senior SFI Professor http://www.math.ethz.ch/~embrechts now Basel III

### Solvency II: Risk Margins and Technical Provisions Peter England

Solvency II: Risk Margins and Technical Provisions Peter England GIRO conference and exhibition 12-15 October 2010 2010 The Actuarial Profession www.actuaries.org.uk Agenda The traditional actuarial view

### Comparing Life Insurer Longevity Risk Transfer Strategies in a Multi-Period Valuation Framework

1 / 28 Comparing Life Insurer Longevity Risk Transfer Strategies in a Multi-Period Valuation Framework Craig Blackburn, Katja Hanewald, Annamaria Olivieri and Michael Sherris Australian School of Business

### CAPITAL ALLOCATION FOR INSURANCE COMPANIES WHAT GOOD IS IT? H e l m u t G r ü n d l, Berlin* and H a t o S c h m e i s e r, Berlin*

CAPITAL ALLOCATION FOR INSURANCE COMPANIES WHAT GOOD IS IT? By H e l m u t G r ü n d l, Berlin* and H a t o S c h m e i s e r, Berlin* SEPTEMBER 23, SECOND DRAFT JEL-KLASSIFICATION: G22, G3, G32 *Institut

### Market-Consistent Valuation of the Sponsor Covenant and its use in Risk-Based Capital Assessment. Craig Turnbull FIA

Market-Consistent Valuation of the Sponsor Covenant and its use in Risk-Based Capital Assessment Craig Turnbull FIA Background and Research Objectives 2 Background: DB Pensions and Risk + Aggregate deficits

### SAVINGS PRODUCTS AND THE LIFE INSURANCE INDUSTRY IN CANADA

SAVINGS PRODUCTS AND THE LIFE INSURANCE INDUSTRY IN CANADA Carl Hiralal 25 November 2004 1 Topics OSFI s Role Canadian Industry Insurance Products in Canada Insurance versus Savings Segregated Funds Universal

### RBC and its Practical Applications to Non-Life Insurance

RBC and its Practical Applications to Non-Life Insurance 27 April 2006 Authors: John McCrossan Colin Manley Declan Lavelle 1.0 Introduction The title of this paper is RBC and its Practical Applications

### Asset Liability Management at Munich Reinsurance Company

Asset Liability Management at Munich Reinsurance Company Helsinki, 17 th November 2004 Bernhard Kaufmann and Jochen Mayer Agenda ALM: Governance and Management The Munich Re ALM-Model: ALM on Macro Level

### Modelling the Claims Development Result for Solvency Purposes

Modelling the Claims Development Result for Solvency Purposes Michael Merz, Mario V. Wüthrich Version: June 10, 008 Abstract We assume that the claims liability process satisfies the distribution-free

### LIFE INSURANCE RATING METHODOLOGY CREDIT RATING AGENCY OF

LIFE INSURANCE RATING METHODOLOGY CREDIT RATING AGENCY OF BANGLADESH LIMITED 1 CRAB S RATING PROCESS An independent and professional approach of the CRAB is designed to ensure reliable, consistent and

### Option Values. Determinants of Call Option Values. CHAPTER 16 Option Valuation. Figure 16.1 Call Option Value Before Expiration

CHAPTER 16 Option Valuation 16.1 OPTION VALUATION: INTRODUCTION Option Values Intrinsic value - profit that could be made if the option was immediately exercised Call: stock price - exercise price Put:

### AGGREGATE CLAIMS, SOLVENCY AND REINSURANCE. David Dickson, Centre for Actuarial Studies, University of Melbourne. Cherry Bud Workshop

AGGREGATE CLAIMS, SOLVENCY AND REINSURANCE David Dickson, Centre for Actuarial Studies, University of Melbourne Cherry Bud Workshop Keio University, 27 March 2006 Basic General Insurance Risk Model where

### Forward Contracts and Forward Rates

Forward Contracts and Forward Rates Outline and Readings Outline Forward Contracts Forward Prices Forward Rates Information in Forward Rates Reading Veronesi, Chapters 5 and 7 Tuckman, Chapters 2 and 16

### 15 April 2015 Kurt Svoboda, CFRO. UNIQA Insurance Group AG Economic Capital and Embedded Value 2014

15 April 2015 Kurt Svoboda, CFRO UNIQA Insurance Group AG Economic Capital and Embedded Value 2014 Economic Capital Embedded Value Sensitivities and other analysis Appendix Assumptions Glossary & Disclaimer

### Market Risk Capital Disclosures Report. For the Quarter Ended March 31, 2013

MARKET RISK CAPITAL DISCLOSURES REPORT For the quarter ended March 31, 2013 Table of Contents Section Page 1 Morgan Stanley... 1 2 Risk-based Capital Guidelines: Market Risk... 1 3 Market Risk... 1 3.1

### Introduction to Options. Derivatives

Introduction to Options Econ 422: Investment, Capital & Finance University of Washington Summer 2010 August 18, 2010 Derivatives A derivative is a security whose payoff or value depends on (is derived

### Insurance: solvency and valuation

Thesis for the Degree of Doctor of Philosophy Insurance: solvency and valuation Jonas Alm Division of Mathematical Statistics Department of Mathematical Sciences Chalmers University of Technology and University

### The Insurance Act, 2015

The Insurance Act, 2015 The Insurance Act, 2015 provides: 158. (1) Every insurer carrying on long-term insurance business shall- (a) as at the end of each financial year cause its appointed actuary to-

### The Multi-Year Non-Life Insurance Risk

The Multi-Year Non-Life Insurance Risk Dorothea Diers, Martin Eling, Christian Kraus und Marc Linde Preprint Series: 2011-11 Fakultät für Mathematik und Wirtschaftswissenschaften UNIVERSITÄT ULM The Multi-Year

Review for Exam 1 Instructions: Please read carefully The exam will have 21 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation

### Matching Investment Strategies in General Insurance Is it Worth It? Aim of Presentation. Background 34TH ANNUAL GIRO CONVENTION

Matching Investment Strategies in General Insurance Is it Worth It? 34TH ANNUAL GIRO CONVENTION CELTIC MANOR RESORT, NEWPORT, WALES Aim of Presentation To answer a key question: What are the benefit of

### Friends Life Limited

Annual PRA Insurance Returns for the year ended 31 December 2014 IPRU(INS) Appendices 9.1, 9.3, 9.4, 9.4A, 9.6 Balance Sheet and Profit and Loss Account Contents Form 2 Statement of solvency - long-term

### Risk Discount Rates for Market Valuation of Life Insurance Business

Contents 1 Introduction... 1 2 Application to Life Office Products... 3 2.1 Generalised Product Description... 3 2.2 Risk Discount Rate for New Business Sales Operations... 4 2.3 Risk Discount Rate for

### Contents. About the author. Introduction

Contents About the author Introduction 1 Retail banks Overview: bank credit analysis and copulas Bank risks Bank risks and returns: the profitability, liquidity and solvency trade-off Credit risk Liquidity

### EEV, MCEV, Solvency, IFRS a chance for actuarial mathematics to get to main-stream of insurance value chain

EEV, MCEV, Solvency, IFRS a chance for actuarial mathematics to get to main-stream of insurance value chain dr Krzysztof Stroiński, dr Renata Onisk, dr Konrad Szuster, mgr Marcin Szczuka 9 June 2008 Presentation

### Asset Liability Management in alargeinsurancecompany

Asset Liability Management in alargeinsurancecompany Andreas N. Lagerås AFA Insurance Asset Management Investment research Seminar KTH 2010-05-17 1(45) Overview Background Assets Liabilities Assets and

### Cover. Optimal Retentions with Ruin Probability Target in The case of Fire. Insurance in Iran

Cover Optimal Retentions with Ruin Probability Target in The case of Fire Insurance in Iran Ghadir Mahdavi Ass. Prof., ECO College of Insurance, Allameh Tabataba i University, Iran Omid Ghavibazoo MS in

### Actuarial and Insurance Solutions Financial Market Analysis at endyear

Actuarial and Insurance Solutions Financial Market Analysis at endyear 2014 15 th January 2015 Audit. Tax. Consulting. Corporate Finance. Contents Executive Summary 1 1 Interest Rates 2 2 Equity Markets

### Financial Options: Pricing and Hedging

Financial Options: Pricing and Hedging Diagrams Debt Equity Value of Firm s Assets T Value of Firm s Assets T Valuation of distressed debt and equity-linked securities requires an understanding of financial

### Interest rate risk and how to manage it. University of Economics, 16/10/2014 Vladimir Sosovicka

Interest rate risk and how to manage it University of Economics, 16/10/2014 Vladimir Sosovicka 2 Content 1. Interest rate risk what is it? 2. Management of interest rate risk: Basic tools (bonds, BPV,

### Life Insurance risk management in the Insurance company : CSOB case studies

Life Insurance risk management in the Insurance company : CSOB case studies Content Topics : case study Life Insurance risk management, 1. Life Insurance 2. Case study what is life insurance product and

### CITIGROUP INC. BASEL II.5 MARKET RISK DISCLOSURES AS OF AND FOR THE PERIOD ENDED MARCH 31, 2013

CITIGROUP INC. BASEL II.5 MARKET RISK DISCLOSURES AS OF AND FOR THE PERIOD ENDED MARCH 31, 2013 DATED AS OF MAY 15, 2013 Table of Contents Qualitative Disclosures Basis of Preparation and Review... 3 Risk

### Embedded Value Report

Embedded Value Report 2012 ACHMEA EMBEDDED VALUE REPORT 2012 Contents Management summary 3 Introduction 4 Embedded Value Results 5 Value Added by New Business 6 Analysis of Change 7 Sensitivities 9 Impact

### BS2551 Money Banking and Finance. Commercial Bank Risk Management. - Competition and deregulation

BS2551 Money Banking and Finance Commercial Bank Risk Management Need for Risk Management Increased complexity of risks faced by banks since 1970s due to: - Competition and deregulation - Asset price volatility

### GLOSSARY. A contract that provides for periodic payments to an annuitant for a specified period of time, often until the annuitant s death.

The glossary contains explanations of certain terms and definitions used in this prospectus in connection with us and our business. The terms and their meanings may not correspond to standard industry

### Guidelines on the valuation of technical provisions

EIOPA-BoS-14/166 EN Guidelines on the valuation of technical provisions EIOPA Westhafen Tower, Westhafenplatz 1-60327 Frankfurt Germany - Tel. + 49 69-951119-20; Fax. + 49 69-951119-19; email: info@eiopa.europa.eu

### Asset/liability Management for Universal Life. Grant Paulsen Rimcon Inc. November 15, 2001

Asset/liability Management for Universal Life Grant Paulsen Rimcon Inc. November 15, 2001 Step 1: Split the product in two Premiums Reinsurance Premiums Benefits Policyholder fund Risk charges Expense

### Quantitative Impact Study 1 (QIS1) Summary Report for Belgium. 21 March 2006

Quantitative Impact Study 1 (QIS1) Summary Report for Belgium 21 March 2006 1 Quantitative Impact Study 1 (QIS1) Summary Report for Belgium INTRODUCTORY REMARKS...4 1. GENERAL OBSERVATIONS...4 1.1. Market

### Using least squares Monte Carlo for capital calculation 21 November 2011

Life Conference and Exhibition 2011 Adam Koursaris, Peter Murphy Using least squares Monte Carlo for capital calculation 21 November 2011 Agenda SCR calculation Nested stochastic problem Limitations of

### Caput Derivatives: October 30, 2003

Caput Derivatives: October 30, 2003 Exam + Answers Total time: 2 hours and 30 minutes. Note 1: You are allowed to use books, course notes, and a calculator. Question 1. [20 points] Consider an investor

### 2013 IAA Education Syllabus

This version was approved at the Council meeting on 26 May 2012 and replaces the 2007 document. 1. Financial Mathematics To provide a grounding in the techniques of financial mathematics and their applications.

### THE MULTI-YEAR NON-LIFE INSURANCE RISK

THE MULTI-YEAR NON-LIFE INSURANCE RISK MARTIN ELING DOROTHEA DIERS MARC LINDE CHRISTIAN KRAUS WORKING PAPERS ON RISK MANAGEMENT AND INSURANCE NO. 96 EDITED BY HATO SCHMEISER CHAIR FOR RISK MANAGEMENT AND

### Risk aggregation in insurance

THESIS FOR THE DEGREE OF LICENTIATE OF ENGINEERING Risk aggregation in insurance Jonas Alm Department of Mathematical Sciences Division of Mathematical Statistics Chalmers University of Technology and

### OPTIONS and FUTURES Lecture 2: Binomial Option Pricing and Call Options

OPTIONS and FUTURES Lecture 2: Binomial Option Pricing and Call Options Philip H. Dybvig Washington University in Saint Louis binomial model replicating portfolio single period artificial (risk-neutral)

### CEIOPS Preparatory Field Study for Life Insurance Firms. Summary Report

CEIOPS-FS-08/05 S CEIOPS Preparatory Field Study for Life Insurance Firms Summary Report 1 GENERAL OBSERVATIONS AND CONCLUSIONS 1.1 Introduction CEIOPS has been asked to prepare advice for the European

### ERM-2: Introduction to Economic Capital Modeling

ERM-2: Introduction to Economic Capital Modeling 2011 Casualty Loss Reserve Seminar, Las Vegas, NV A presentation by François Morin September 15, 2011 2011 Towers Watson. All rights reserved. INTRODUCTION

### FINANCIAL PLANNING ASSOCIATION OF MALAYSIA

FINANCIAL PLANNING ASSOCIATION OF MALAYSIA MODULE 4 INVESTMENT PLANNING Course Objectives To understand the concepts of risk and return, the financial markets and the various financial instruments available,

### Best Estimate of the Technical Provisions

Best Estimate of the Technical Provisions FSI Regional Seminar for Supervisors in Africa on Risk Based Supervision Mombasa, Kenya, 14-17 September 2010 Leigh McMahon BA FIAA GAICD Senior Manager, Diversified

### The Master of Science in Finance (English Program) - MSF. Department of Banking and Finance. Chulalongkorn Business School. Chulalongkorn University

The Master of Science in Finance (English Program) - MSF Department of Banking and Finance Chulalongkorn Business School Chulalongkorn University Overview of Program Structure Full Time Program: 1 Year

### Swiss Solvency Test in Non-life Insurance

Swiss Solvency Test in Non-life Insurance Luder Thomas Federal Office of Private Insurance Schwanengasse 2 3003 Bern Switzerland Tel. ++4 3 325 0 68 Fax. ++4 3 323 7 56 thomas.luder@bpv.admin.ch July 28,

Econ 497 Barry W. Ickes Spring 2007 Midterm Exam:Answer Sheet 1. (25%) Consider a portfolio, c, comprised of a risk-free and risky asset, with returns given by r f and E(r p ), respectively. Let y be the

### CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

Chapter - The Term Structure of Interest Rates CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future

### WACC and a Generalized Tax Code

WACC and a Generalized Tax Code Sven Husmann, Lutz Kruschwitz and Andreas Löffler version from 10/06/2001 ISSN 0949 9962 Abstract We extend the WACC approach to a tax system having a firm income tax and

### Security Analysis and Portfolio Management FIN-321-TE

Security Analysis and Portfolio Management FIN-321-TE This TECEP is an introduction to investment alternatives, security analysis, and portfolio construction. Topics include: the environment in which investment

### CHAPTER 22 Options and Corporate Finance

CHAPTER 22 Options and Corporate Finance Multiple Choice Questions: I. DEFINITIONS OPTIONS a 1. A financial contract that gives its owner the right, but not the obligation, to buy or sell a specified asset

### CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

CHAPTER : THE TERM STRUCTURE OF INTEREST RATES CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future

### KLP BOLIGKREDITT AS Interim report Q4 2015

KLP BOLIGKREDITT AS Interim report Q4 2015 INCOME STATEMENT BALANCE SHEET NOTES Contents KLP Boligkreditt AS Report from the Board of directors 3 Income statement 4 Balance sheet 5 Statement of changes

### IAA PAPER VALUATION OF RISK ADJUSTED CASH FLOWS AND THE SETTING OF DISCOUNT RATES THEORY AND PRACTICE

Introduction This document refers to sub-issue 11G of the IASC Insurance Issues paper and proposes a method to value risk-adjusted cash flows (refer to the IAA paper INSURANCE LIABILITIES - VALUATION &

### Marshall-Olkin distributions and portfolio credit risk

Marshall-Olkin distributions and portfolio credit risk Moderne Finanzmathematik und ihre Anwendungen für Banken und Versicherungen, Fraunhofer ITWM, Kaiserslautern, in Kooperation mit der TU München und

### Market Value Based Accounting and Capital Framework

Market Value Based Accounting and Capital Framework Presented by: Erik Anderson, FSA, MAAA New York Life Insurance Company Prannoy Chaudhury, FSA, MAAA Milliman 2014 ASNY Meeting November 5, 2014 1 07

### Embedded Value in Life Insurance

Embedded Value in Life Insurance Gilberto Castellani Università di Roma La Sapienza Massimo De Felice Università di Roma La Sapienza Franco Moriconi Università di Perugia Claudio Pacati Università di Siena

### Bond Valuation. Capital Budgeting and Corporate Objectives

Bond Valuation Capital Budgeting and Corporate Objectives Professor Ron Kaniel Simon School of Business University of Rochester 1 Bond Valuation An Overview Introduction to bonds and bond markets» What

### by the symbol u(w,t).

1981 General Insurance Convention RISK THEORY AND THE DETERMINATION OF SOLVENCY 1_. Introduction 1.1 The use of Risk Theory in General Insurance goes back an extremely long way. Barrows (1835) distinguished

### Contents. List of Figures. List of Tables. Acknowledgments PART I INTRODUCTION 1

List of Figures List of Tables Acknowledgments Preface xv xix xxi xxiii PART I INTRODUCTION 1 1 The Evolution of Financial Analysis 3 1.1 Bookkeeping 3 1.2 Modern finance 8 1.3 Departments, silos and analysis

### AISAM-ACME study on non-life long tail liabilities

AISAM-ACME study on non-life long tail liabilities Reserve risk and risk margin assessment under Solvency II 17 October 2007 Page 3 of 48 AISAM-ACME study on non-life long tail liabilities Reserve risk

### CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on long-term bonds are geometric averages of present and expected future short rates. An upward sloping curve is

### Notes to the consolidated financial statements Part E Information on risks and relative hedging policies

SECTION 2 RISKS OF INSURANCE COMPANIES 2.1 INSURANCE RISKS Life branch The typical risks of the life insurance portfolio (managed by EurizonVita, EurizonLife, SudPoloVita and CentroVita) may be divided

### CEIOPS-DOC-33/09. (former CP 39) October 2009

CEIOPS-DOC-33/09 CEIOPS Advice for Level 2 Implementing Measures on Solvency II: Technical provisions Article 86 a Actuarial and statistical methodologies to calculate the best estimate (former CP 39)

### SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS

SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS This page indicates changes made to Study Note FM-09-05. April 28, 2014: Question and solutions 61 were added. January 14, 2014:

### This paper is not to be removed from the Examination Halls

~~FN3023 ZA d0 This paper is not to be removed from the Examination Halls UNIVERSITY OF LONDON FN3023 ZA BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the Social Sciences,

### Investment Assumptions Used in the Valuation of Life and Health Insurance Contract Liabilities

Educational Note Investment Assumptions Used in the Valuation of Life and Health Insurance Contract Liabilities Committee on Life Insurance Financial Reporting September 2014 Document 214099 Ce document

### Modelling and Management of Tail Risk in Insurance

Modelling and Management of Tail Risk in Insurance IMF conference on operationalising systemic risk monitoring Peter Sohre, Head of Risk Reporting, Swiss Re Washington DC, 27 May 2010 Visit of ntuc ERM

QUADRANT SKEW CAPITAL Syllabus OVERVIEW Quadrant Skew Capital s Equity Research Program focuses on material, content and skills that are directly applicable to real-world application. Our program provides

### How to Model Operational Risk, if You Must

How to Model Operational Risk, if You Must Paul Embrechts ETH Zürich (www.math.ethz.ch/ embrechts) Based on joint work with V. Chavez-Demoulin, H. Furrer, R. Kaufmann, J. Nešlehová and G. Samorodnitsky

### REGULATION ON MEASUREMENT AND ASSESSMENT OF CAPITAL REQUIREMENTS OF INSURANCE AND REINSURANCE COMPANIES AND PENSION COMPANIES

REGULATION ON MEASUREMENT AND ASSESSMENT OF CAPITAL REQUIREMENTS OF INSURANCE AND REINSURANCE COMPANIES AND PENSION COMPANIES Official Gazette of Publication: 19.01.2008 26761 Issued By: Prime Ministry

### INDUSTRIAL-ALLIANCE LIFE INSURANCE COMPANY. FIRST QUARTER 2000 Consolidated Financial Statements (Non audited)

INDUSTRIAL-ALLIANCE LIFE INSURANCE COMPANY FIRST QUARTER 2000 Consolidated Financial Statements (Non audited) March 31,2000 TABLE OF CONTENTS CONSOLIDATED INCOME 2 CONSOLIDATED CONTINUITY OF EQUITY 3 CONSOLIDATED

### Should Life Insurers buy CoCo Bonds? - Regulatory Effects Implied by the Solvency II Standards

Should Life Insurers buy CoCo Bonds? - Regulatory Effects Implied by the Solvency II Standards Helmut Gründl, Tobias Niedrig International Center for Insurance Regulation (ICIR) and Center of Excellence

### C(t) (1 + y) 4. t=1. For the 4 year bond considered above, assume that the price today is 900\$. The yield to maturity will then be the y that solves

Economics 7344, Spring 2013 Bent E. Sørensen INTEREST RATE THEORY We will cover fixed income securities. The major categories of long-term fixed income securities are federal government bonds, corporate

### Effective Financial Planning for Life Insurance Companies

6 th Global Conference of Actuaries Effective Financial Planning for Life Insurance Companies Presentation by Kim Hoong CHIN Senior Manager and Consultant Asia Financial Services Topics Recent worldwide

### Fundamentals of Actuarial Mathematics. 3rd Edition

Brochure More information from http://www.researchandmarkets.com/reports/2866022/ Fundamentals of Actuarial Mathematics. 3rd Edition Description: - Provides a comprehensive coverage of both the deterministic

### Goldman Sachs Financials Conference Surviving in a low interest rate environment

Goldman Sachs Financials Conference Surviving in a low interest rate environment Prof. Dr. Michael Koller, CRO and Group Chief Acturay Rome, 18 June 2003 Management Summary Understanding Economic Principles?

### Basel Committee on Banking Supervision. An Explanatory Note on the Basel II IRB Risk Weight Functions

Basel Committee on Banking Supervision An Explanatory Note on the Basel II IRB Risk Weight Functions July 2005 Requests for copies of publications, or for additions/changes to the mailing list, should

### SOA Annual Symposium Shanghai. November 5-6, 2012. Shanghai, China. Session 2a: Capital Market Drives Investment Strategy.

SOA Annual Symposium Shanghai November 5-6, 2012 Shanghai, China Session 2a: Capital Market Drives Investment Strategy Genghui Wu Capital Market Drives Investment Strategy Genghui Wu FSA, CFA, FRM, MAAA

### ACCOUNTING STANDARDS BOARD DECEMBER 2004 FRS 27 27LIFE ASSURANCE STANDARD FINANCIAL REPORTING ACCOUNTING STANDARDS BOARD

ACCOUNTING STANDARDS BOARD DECEMBER 2004 FRS 27 27LIFE ASSURANCE FINANCIAL REPORTING STANDARD ACCOUNTING STANDARDS BOARD Financial Reporting Standard 27 'Life Assurance' is issued by the Accounting Standards

### The International Certificate in Banking Risk and Regulation (ICBRR)

The International Certificate in Banking Risk and Regulation (ICBRR) The ICBRR fosters financial risk awareness through thought leadership. To develop best practices in financial Risk Management, the authors

### KLP BOLIGKREDITT AS Interim report Q1 2016

KLP BOLIGKREDITT AS Interim report Q1 2016 INCOME STATEMENT BALANCE SHEET NOTES Contents KLP Boligkreditt AS Report from the Board of directors 3 Income statement 4 Balance sheet 5 Statement of changes

### Projection of the With-Profits Balance Sheet under ICA+ John Lim (KPMG) & Richard Taylor (AEGON) 11 November 2013

Projection of the With-Profits Balance Sheet under ICA+ John Lim (KPMG) & Richard Taylor (AEGON) 11 November 2013 Introduction Projecting the with-profits business explicitly is already carried out by

### SESSION/SÉANCE : 37 Applications of Forward Mortality Factor Models in Life Insurance Practice SPEAKER(S)/CONFÉRENCIER(S) : Nan Zhu, Georgia State

SESSION/SÉANCE : 37 Applications of Forward Mortality Factor Models in Life Insurance Practice SPEAKER(S)/CONFÉRENCIER(S) : Nan Zhu, Georgia State University and Illinois State University 1. Introduction

### A Note on the Ruin Probability in the Delayed Renewal Risk Model

Southeast Asian Bulletin of Mathematics 2004 28: 1 5 Southeast Asian Bulletin of Mathematics c SEAMS. 2004 A Note on the Ruin Probability in the Delayed Renewal Risk Model Chun Su Department of Statistics

### Solvency Management in Life Insurance The company s perspective

Group Risk IAA Seminar 19 April 2007, Mexico City Uncertainty Exposure Solvency Management in Life Insurance The company s perspective Agenda 1. Key elements of Allianz Risk Management framework 2. Drawbacks