Electronic Market Making: Initial Investigation

Transcription

1 Elecronic Marke Making: Iniial Invesigaion Yuriy Nevmyvaka The Roboics Insiue Carnegie Mellon Universiy Pisburgh, PA Kaia Sycara The Roboics Insiue Carnegie Mellon Universiy Pisburgh, PA Duane J. Seppi GSIA Carnegie Mellon Universiy Pisburgh, PA Absrac This paper esablishes an analyical foundaion for elecronic marke making. Creaing an auomaed securiies dealer is a challenging ask wih imporan heoreical and pracical implicaions. Our main ineres is a normaive auomaion of he marke maker s aciviies, as opposed o explanaory modeling of human raders, which was he primary concern of earlier work in his domain. We use a simple class of non-predicive rading sraegies o highligh he fundamenal issues. These sraegies have a heoreical foundaion behind hem and serve as a showcase for he decisions o be addressed: deph of quoe, quoe posiioning, iming of updaes, invenory managemen, and ohers. We examine he impac of various parameers on he marke maker s performance. Alhough we conclude ha such elemenary sraegies do no solve he problem compleely, we are able o idenify he areas ha need o be addressed wih more advanced ools. We hope ha his paper can serve as a firs sep in rigorous examinaion of he dealer s aciviies, and will be useful in disciplines ouside of Finance, such as Agens, Roboics, and E-Commerce. 1 Inroducion Wha is marke making? In modern financial markes, marke makers (or dealers) are agens who sand ready o buy and sell securiies. The res of marke paricipans are herefore guaraneed o always have a counerpary for heir ransacions. This renders markes more orderly and prices less volaile. Marke maker are remuneraed for heir services by being able o buy low and sell high. Insead of a single price a which any rade can occur, dealers quoe wo prices a bid (dealer s purchase, cusomer s sale) and an ask (dealer s sale, cusomer s purchase). The ask is higher han he bid, and he difference beween he wo is called he spread he dealer s source of revenue. Wha are he benefis of auomaing his aciviy? This is a challenging decision problem: how can a machine updae he bid-ask spread, anicipaing or reacing o changes in he supply and demand for a securiy? This seing is also a grea es bed for Machine Learning and Saisical echniques. Creaion of an elecronic dealer is a sab a he main goal of AI: replicaion of a human decision process, which is nooriously difficul o model or imiae. From a more pragmaic poin of view, elecronic marke makers could render securiies professionals more producive and markes more sable. Auomaed dealers, if designed properly, will no engage in marke manipulaions and oher securiies laws violaions ha recenly resuled in a number of dealer-cenered scandals in boh he NASDAQ [3] and NYSE [9]. Also, a more in-deph undersanding of he dealer s behavior will give us beer guidance in exreme siuaions (marke crises) and will faciliae he regulaory oversigh. Finally, we expec auomaed marke making o have an impac on oher disciplines ha employ various marke mechanisms o solve disribued problems: Roboics [15], E-Commerce [7], Inelligen Agens [12], ec. The goal of his paper is o esablish an analyical framework for elecronic marke making, using a simple class of sraegies o highligh some cenral issues and challenges in his domain. The paper is organized as follows. Secion 2 explains where he presen effor is siuaed relaively o oher research in his area. In Secion 3, we describe our experimenal seup. Secion 4 presens a simple model of elecronic marke making and a general axonomy of possible sraegies. Secion 5 makes a case for so-called nonpredicive marke-making sraegies, while Secion 6 presens he relevan experimenal resuls. We conclude wih a recap of imporan issues and a descripion of fuure work. 2 Relaed Work Comparison Auomaion of dealer s aciviies was suggesed more han hree decades ago [2] and is an imporan par of Marke Microsrucure an area ha has evolved ino an independen subfield of Finance. The bulk of previous research on marke making is mosly concerned wih he sources and componens of he bidask spread. A number of models have been developed o explain he evoluion of he spread, incorporaing various facors ha affec he marke maker s decision process, such as invenory [13], informaion [4], volailiy [6], risk aversion, compeiion [14], and many ohers [8]. The problem wih such approaches is ha

2 hey are mosly explanaory in naure. The relevan work in he Compuer Science communiy is more limied. Marke making has been adoped as a es-bed for new Machine Learning echniques [11] wih a goal o demonsrae he general effeciveness of a learning algorihm, as opposed o reaing marke making as a problem ha requires solving. Also, empirical work has demonsraed he limiaions of hard-coding markemaking rules ino an algorihm [5]. The moivaion behind our approach is fundamenally differen from ha of previous research. Since we are ineresed in creaing an elecronic marke maker, we are much more concerned abou fuure performance. Therefore, our primary goal is o opimally change he spread over he nex ieraion insead of finding he bes model for pas ransacions. We are rying o creae somehing much more normaive (as opposed o explanaory): o deermine which facors are imporan for making he spread updae, and o capure he decision process of a dealer. 3 Experimenal Seup In our experimens, we used he Penn Exchange Simulaor (PXS) sofware developed a he Universiy of Pennsylvania, which merges acual orders from he Island elecronic marke wih arificial orders generaed by elecronic rading agens [1]. Island is wha is called an Elecronic Communicaion Nework (ECN). ECNs are somewha differen from radiional sock exchanges such as NYSE or he NASDAQ OTC marke. NYSE and NASDAQ employ securiies dealers o provide liquidiy and mainain orderly markes, and use boh marke and limi orders. A marke order is an insrucion from a clien o he dealer o buy or sell a cerain quaniy of sock a he bes available price, whereas a limi order asks for a ransacion a a specified or more advanageous price. Therefore, marke orders guaranee he execuion, bu no he price a which ransacion will occur, whereas limi orders guaranee a cerain price, bu ransacion may never happen. Island ECN is a purely elecronic marke, which only uses limi orders and employs no designaed middlemen. All liquidiy comes from cusomers limi orders ha are arranged in order books (essenially wo prioriy queues ordered by price) as shown in Figure 1a (limi price number of shares). If a new order arrives, and here are no orders on he opposie side of he marke ha can saisfy he limi price, hen he order is being enered ino he book. In Figure 1b, a new buy order for 1 shares a $25.2 or less has arrived, bu he bes sell order is for $25.3 or more; hus no ransacion is possible, and he new order is enered ino he buy queue. When anoher buy order arrives for 25 shares a $25.4 or less, i ges ransaced (or crossed) wih he ousanding orders in he sell queue: 15 shares are bough a $25.3 and anoher 1 shares are bough a $25.35 (Figure 1c). This demonsraes ha even hough here are no designaed marke orders in ECNs, immediae and guaraneed execuion is sill possible by specifying a limi price ha falls inside he opposie order book. All crossing is performed by a compuer respecing he price and ime prioriy, wihou any inermediaries. Sell Orders Buy Orders (c) Figure 1. Wha PXS does is simple: a each ieraion, i rerieves a snapsho of he Island s order book, gahers all of he limi orders from rading agens in he simulaion, and hen merges all he orders (real and arificial) according o he ECN rules described above: some orders ransac and some ge enered ino he book. When ransacions happen, agens are noified abou he changes in heir invenory and cash, and he new merged order book becomes available o all he agens o sudy and make decisions. This new order book is he sae represenaion of he simulaor s marke, which can be differen from he Island marke because he orders from elecronic raders are presen only in he simulaor. The inheren problem wih such seup is ha Island (real-world) raders will no reac o he acions of he raders in he simulaor, which can lead o a disconnec beween he wo markes. This implies ha in order for he experimen o remain meaningful, he simulaor raders have o remain low impac i.e. heir acions should no move he simulaed price significanly away from he Island price. We enforce his propery by prohibiing he paricipaing agens from accumulaing a posiion in excess of 1, shares eiher shor or long. Such a simple rule ges he job done surprisingly well. To pu hing in perspecive, daily volume in he simulaor reaches many million shares (acively raded MSFT is being used). As saed before, PXS does no have marke orders ha flow hrough he dealers, or any designaed dealers a all, for ha maer. This can lead o a conclusion ha such seup is ill-suied for sudying he marke maker s behavior. Bu we have o draw a disincion beween marke making as an insiuion (as seen on he NYSE floor) vs. marke making as a rading sraegy (used on proprieary rading desks and cerain OTC dealing operaions). The former can be inerpreed as public service, where he marke maker has cerain obligaions. He is supposed o be compensaed by he bid-ask spread, bu because of heavy regulaions ha proec cusomers, he dealer ofen finds himself being resriced in rading opporuniies, which limis his profis [9]. Alernaively, marke making can be

3 inerpreed as a sraegy where a rader ries o keep his sock posiion around zero (being marke neural ) and o profi from shor-erm price flucuaions. As far as low profile rading goes, he marke maker is no supposed o move markes: he NYSE dealers are explicily prohibied from doing so by he negaive obligaion principle. Thus, our seup is well suied for sudying marke making as a sraegy, which also happens o be he main par of marke making as an insiuion. 4 Marke Making: A Model We decompose he problem facing he elecronic marke maker ino wo componens: esablishing he bid-ask spread and updaing i. We furher subdivide he updae mehods ino predicive and non-predicive. The primary objecive of a dealer is o manage he bidask spread: i has o be posiioned in such a way ha rades occur a he bid as ofen as a he ask, hus allowing he dealer o buy low and sell high. (We will examine hese mechanics in Secion 5). In order for his o happen, he quoes have o sraddle he rue price of he securiy [6] and be posiioned as close o i as possible. However, he rue price is an elusive concep, difficul o deermine or model. Therefore, he firs decision for he marke maker (eiher human or arificial) is where o esablish he iniial spread. Top sell Inside Marke Top buy Top sell Dealer s ask Bid-Ask Spread Dealer s bid Top buy Figure 2. There are wo ways o approach his decision. The firs, hard way is o perform he acual valuaion of he securiy being raded: for a sock, ry o deermine he value of he company using discouned cash flows, raios, ec.; for a bond, find he presen value of he promised paymens, and so on. If here is no esablished marke, or he marke is very illiquid, hen valuaion may be he only approach. Forunaely, he majoriy of modern securiies markes employ limi orders in some capaciy. The wo queues of he order book should be an accurae represenaion of he curren supply (sell queue) and demand (buy queue) for he securiy. Presened wih such supply-demand schedule, he marke maker ries o deermine he consensual value. In he simples case, he dealer can observe he op of each book he bes (highes) buy and he bes (lowes) sell also known as he inside marke. He hen assumes ha he marke s consensus abou he price lies somewhere beween hese wo numbers. In Figure 2a he bes bid is $25.21, and he bes ask is $25.3 (he inside marke is $ ), and he rue price of he sock is in his inerval. Now, he marke maker can use he op of each book as a reference poin for posiioning his iniial quoes a $ , for example (Figure 2b) and hen updae his spread as he book evolves wih new arrivals, ransacions and cancellaions. Updaing he spread is a he hear of marke making. While he order book is informaive abou he consensus price of he securiy, i ofen fails o provide sufficien liquidiy, hus creaing demand for marke makers. We classify updae sraegies ino wo caegories. The firs aemps o foresee he upcoming marke movemens (eiher from he order book misbalances or from shor-erm paerns), and adjus he spread according o hese expecaions. The second group reasons solely on he informaion abou he curren inside marke. These non-predicive sraegies are inherenly simpler, and, herefore, beer suied for our inroducory examinaion of elecronic marke making. 5 Non-Predicive Sraegies In order o make he case ha he non-predicive sraegies are worh considering, le s examine in deail how he marke maker earns money. Following he movemen of he sock price over several hours, i is easy o discern some paerns: going up, down, back up, and so on. Bu if we ake an exremely shor ime period (seconds or fracions of a second), i becomes apparen ha he sock consanly oscillaes up and down around a more persisen (longer-erm) movemen. If he price rises consisenly over an hour, i doesn mean ha everyone is buying; selling is going on as well, and he ransacion price (along wih he inside marke) moves down as well as up. Figure 3 illusraes his: while here is an upward movemen (he doed line), we can see he emporal evoluion of he order book where ransacions happen a he op of he buy queue, hen he sell queue, hen buy, hen sell again. By mainaining his quoes on boh sides of he marke, a or close o he op of each order book, he marke maker can expec o ge hi a his bid roughly as ofen as a he ask because of hese flucuaions. This way, afer buying a he bid (low) and selling a he ask (high), he dealer receives he profi equal o he bid-ask spread for he wo rades, or half-he-spread per rade. In he conex of Figure 3, suppose ha he op order in each queue is he dealer s; he dealer buys a $25.1, hen sells a $25.18 (8 cens per share profi), buys a $25.16 and sells a $25.26 (1 cens profi). If each ransacion involves 1, shares, and all his happens over several seconds, hen marke making can be quie profiable. Having undersood he naure of he dealer s income, we can re-formulae his ask: adjus he bid-ask spread in such a way ha he orders generaed by oher marke paricipans will ransac wih he dealer s bid quoe and he dealer s ask quoe wih he same frequency. In our

4 example, we are looking for an algorihm o mainain he dealer s quoes on op of each queue o capure all incoming ransacions. The sock price is seadily going up overall, while flucuaing around his general climb, so if he marke maker wans o mainain profiabiliy, hen his spread should also coninuously move up sraddling he sock price Figure 3. How can he dealer ell a any given poin looking forward ha i s ime o move he spread up and by how much? The non-predicive family of elecronic rading sraegies would argue ha he canno and need no do so. I posulaes ha while here are some paerns globally, he local evoluion of he sock price is a random walk. If his random walk his he bid roughly as ofen as i his he ask, hen he marke maker makes a profi. This means ha an upick in he sock price is as likely o be followed by a downick as by anoher upick idea of efficien markes wih shor-erm liquidiy imbalances. If he above assumpion holds, and if he dealer is able o operae quickly enough, hen he rading sraegy is very simple. All he dealer has o do is mainain his bid and ask quoes symmerically disan from he op of each book. As he book evolves, he marke maker has o revise his quoes as quickly as possible, reacing o changes in such a way ha profiabiliy is mainained. In principle, he dealer should be marke neural i.e. he doesn care wha direcion he marke is headed he is only concerned abou booking he spread. On he oher hand, he dealer is ineresed in knowing how he inside marke will change over he nex ieraion in order o updae his quoes correcly. The way he nonpredicive sraegies address his is by assuming ha he inside marke afer one shor ime sep will remain roughly a he same level (ha s he bes guess we can make). Therefore, being one sep behind he marke is good enough if one can reac quickly o he changes. Such is he heory behind his class of sraegies, bu in pracice his urns ou o be more complicaed. 6 Implemenaion and Resuls Here is a general ouline of an algorihm ha implemens he non-predicive sraegy; a each ieraion: (1) Rerieve he updaed order book; (2) Locae an inside marke; (3) Submi new quoes (buy and sell limi orders), posiioned relaively o he inside marke; (4) Cancel previous quoe. As i should be clear from his descripion and he heoreical discussion above, here are hree main facors, or parameers, ha deermine a non-predicive sraegy: posiion of he quoe relaive o he inside marke, deph of he quoe (number of shares in he limi order), and he ime beween quoe updaes Timing Timing is, perhaps, he simples ou of he hree parameers o address. Our experimenal resuls are consisen wih he heoreical model from Secion 5: faser updaes ranslae ino higher profis. The dealer wans o respond o changes in he marke as soon as possible, and herefore, he ime beween he updaes should be as close o zero as he sysem allows. The implicaion of his rule is ha updae ime should cerainly be minimized when designing an elecronic marke maker. The compuaional cycle mus be performed as fas as possible, and he communicaion beween he dealer and he marke should also be sped up. Our experimen shows ha i s he laer issue ha is a more imporan boleneck, plus i s he one harder o conrol. The compuaional cycle for a simple sraegy is inherenly shor (under 1 second), bu i akes abou 3 5 seconds for a submied order o show up in he book, and abou he same delay for he order o ge cancelled (if no ransaced) afer i appears in he book. While hese delays are no unreasonable by he real world s sandards, hey are no negligible. This is one of he fricions in marke implemenaion, which should no be overlooked: he dealer wans o access he marke as quickly as possible, bu such delays can preven him from operaing on a scale shor enough o capure he small flucuaions. Therefore, oher sysems where hese delays can be decreased can poenially be more effecive and produce beer resuls han our simulaed seup Quoe Posiioning Posiion of he quoe relaive o he res of he order book is he mos imporan parameer. We use a simple disance meric: number of cens by which he dealer s quoe differs from he op [non-dealer] order in he appropriae book. We sared our sraegy implemenaion wih a well-known, albei conroversial pracice of penny jumping. In general, penny jumping occurs when a dealer, afer enering his cusomer s order ino he order book, submis his own order, which improves he cusomer s limi price by a very small amoun. The dealer effecively seps in fron of his cusomer: he cusomer s poenial counerpary will ransac wih he dealer insead. Such pracice is no illegal (because he dealer does provide a price improvemen over he original order), bu is considered unehical, and became he cener of he recen NYSE invesigaion [9]. In our case, we are simply undercuing he curren inside marke (or he de faco

5 bid-ask spread) by one cen on boh sides. Figure 2a shows ha if he inside marke is , our marke maker s orders will make i (he size of he bid-ask spread goes from 9 o 7 cens). This way, he dealer is guaraneed o paricipae in any incoming ransacion up o he size specified in he deph of his quoe. We expec he following behavior from his sraegy: he revenue (P&L) should rise slowly over ime (since profi per share is iny), while he invenory (I) ough o flucuae around zero (see Figure 4a). We observe, however, ha in our es se a ypical rading day looks like Figure 4b: he sraegy gradually loses money. P&L I P&L I Figure 4. The fundamenal problem is ha while we base our decision on he book a ime, our orders ges placed in he book a 1, which may or may no be differen from he original book. The non-predicive sraegy places an implici be ha he wo books will be close a leas enough o preserve he profiable propery of dealing. Wha acually happens in our ess, is ha he inside marke is already igh, plus he book changes somewha over he 3 second delay, and hus, ofenimes, boh he bid and he ask placed a end up on he same side of he marke a 1 (Figure 5a). Then one of he orders ransacs, and he oher ges buried deep in he order book. If we find ourselves in his siuaion on a regular basis, we end up paying he spread insead of profiing from i. This explains why our acual P&L paern mirrors he paern we expeced. This experimen highlighs he hree challenges for elecronic marke making in any seing: (1) making decisions in one book, acing in anoher; (2) marke fricions aggravae his disconnec; and, (3) spreads are exremely igh leaving lile or no profi margin [1]. Does his mean ha he non-predicive sraegies are inherenly money-losing? No a all one modificaion solves he hird issue and miigaes he firs wo. We found ha insead of undercuing he inside marke, i is more profiable o pu he quoes deeper in heir respecive books. The dealer s spread is wider now resuling in higher margins, plus even if he quoes ge pu ino he book wih a delay, hey sill manage o sraddle he inside marke and preserve he buy low, sell high propery. Figure 5b shows he exac same scenario as Figure 5a, bu wih wider dealer quoes. Wider spreads lead o higher profi margins, bu less volume flowing hrough he dealer. One has o find a balance beween hese wo componens of he revenue. We deermined ha puing he quoes 1-3 cens away from he inside marke works well, and alleviaes he concerns ha make penny jumping unprofiable. We also deermined ha he hird fundamenal parameer he deph of quoe can also increase he dealer s volume and hus his profiabiliy: he deeper he quoe he more socks will flow hrough he dealer wih each ransacion. However, increasing he volume o an arbirary level has consequences for dealer s invenory Figure Invenory Managemen In heory, he marke maker should buy roughly as frequenly as he sells, which implies ha his invenory should flucuae around zero. In pracice, however, his doesn always work ou. If a sock price is going up consisenly for some period of ime, he dealer s ask ends up geing hi more ofen han his bid. If he dealer s quoe is deep and/or close o he inside marke he winds up wih a growing shor posiion in a rising sock he is aking a loss. Plus, even he main assumpion behind he non-predicive sraegies can fail: when a sock crashes, here are acually no buyers in he markeplace, and our enire markemaking model is simply no valid any more. Finally, if a dealer accumulaes a large posiion in a sock, he becomes vulnerable o abrup shifs in supply and demand i.e. if he has a significan long posiion, and he sock price suddenly falls, hen he s aking a loss. In brief, here is a rade-off: on one hand, he dealer wans o have a large invenory o move back and forh from one side of he marke o he oher making profi, bu hen he doesn wan o become exposed by having a posiion ha canno be easily liquidaed or reversed. To reconcile hese conflicing goals, some rules have o be pu in place o manage he dealer s holdings. We have implemened and esed a number of such approaches. The disance o he inside marke proved o be he more effecive, since i s ied boh o he invenory and profiabiliy. If here is oo much buying (he dealer s ask is being hi oo ofen, and he accumulaes a shor posiion), hen moving he ask deeper ino he sell book compensaes for his. Also, if he sock is going in one direcion consisenly, his approach will force he spread o be coninuously adjused, using he invenory

6 misbalance as a signal. We achieved good resuls wih he formula QuoeDisance = MinimumDisance + alpha * max(, Invenory IniialLimi)/Invenory * MinimumDisance. When he posiion is wihin he IniialLimi, he quoe is always se MinimumDisance away from he marke, bu if he invenory ges ouside he limi, he quoe moves furher away, encouraging he invenory s movemen in he opposie direcion. 7 Analysis and Conclusion Implemening and esing he non-predicive markemaking sraegies, we arrived a a number of conclusions: faser updaes allow o follow he marke more closely and increase profiabiliy; o comba narrow spread and ime delays, we can pu he quoe deeper ino he book, alhough a he expense of he rading volume; rading volume can be increased wih deeper quoes; invenory can be managed effecively by resizing he spread. However, non-predicive sraegies do no solve he marke-making problem compleely. Figure 6 exemplifies one general shorcoming of nonpredicive sraegies: a he open, he price keeps going up, he marke maker canno ge his quoes ou of he way fas enough, accumulaes a large shor posiion, and loses a lo of money. All his happens in 1 minues. This goes back o one fundamenal problem: here are imes when he shor-erm flucuaions in which he non-predicive sraegies are rooed jus aren here. The only way o address his is o use some predicive insrumens order book misbalances, pas paerns, or boh in order o be prepared for hese sreaks. MSFT Figure 6. Even wih his inheren weakness, he non-predicive sraegies have some clear pracical advanages. Firs, hey are simple and compuaionally cheap, bu, a he same ime, a human rader can never replicae hem. Their performance can be improved by speeding up he access o he marke, or by applying hem o less liquid socks. Their use of he inside marke as he only decision anchor makes hem indifferen abou he composiion of he rading crowd. And, finally, he problemaic siuaions, described above can be handled by special cases o boos he overall performance. In his paper, we have presened a srucured framework for reasoning abou he elecronic marke making and analyzed a number of fundamenal issues in his domain using a simple class of sraegies as an example. While P&L -15, Invenory -1, we have no provided all he answers, our main goal was o frame elecronic marke making as a coheren problem and o highligh he poins ha mus be addressed in order for his problem o be solved. We believe ha his is an ineresing and promising area, and ha advances in he elecronic marke making will be useful in disciplines beyond Finance. Bibliography 1. Barclay M., Chrisie W., Harris, J., Kandel, E., and Schulz, P., The Effecs of Marke Reform on he Trading Coss and Deph of NASDAQ Socks, Journal of Finance 54, Black F., Toward a Fully Auomaed Exchange, Financial Analyss Journal, Nov.-Dec Chrisie, W. and Schulz, P., Why do NASDAQ marke makers avoid odd-eighh quoes? Journal of Finance 49, , Glosen, L., and Milgrom, P., Bid, Ask and Transacion Prices in a Specialis Marke wih Heerogeneously Informed Traders, Journal of Financial Economics 14, Hakansson, N.H., Beja, A., and Kale, J., On he Feasibiliy of Auomaed Marke Making by a Programmed Specialis, The Journal of Finance, Vol. 4, March Ho, T. and Soll, H., Opimal Dealer Pricing Under Transacions and Reurn Uncerainy, Journal of Financial Economics 9, Huang, P., Scheller-Wolf, A., and Sycara, K., Design of a Muli-uni Double Aucion E-marke, Compuaional Inelligence, vol. 18, No. 4, Huang, R., Soll, H., The Componens of he Bid-Ask Spread: A General Approach, The Review of Financial Sudies, Vol. 1, Winer Ip, G. and Craig, S., NYSE s Specialis Probe Pus Precious Asse a Risk: Trus, The Wall Sree Journal, April 18, Kearns, M. and Oriz, L., The Penn-Lehman Auomaed Trading Projec, IJCAI TADA Workshop, Kim, A.J., Shelon, C.R., Modeling Sock Order Flows and Learning Marke-Making from Daa, Technical Repor CBCL Paper #217/AI Memo #22-9, M.I.T., Cambridge, MA, June Klusch, M. and Sycara, K., Brokering and Machmaking for Coordinaion of Agen Socieies: A Survey. In Coordinaion of Inerne Agens, A. Omicini e al. (eds.), Springer, Madhavan, A., and Smid, S., An Analysis of Changes in Specialis Invenories and Quoaions, The Journal of Finance, Vol. 48, Dec Seppi, D., Liquidiy Provision wih Limi Orders and Sraegic Specialis, The Review of Financial Sudies, Vol. 1, Issue 1, Zlo, R.M., Senz, A., Dias, M.B., and Thayer, S., Muli-Robo Exploraion Conrolled by a Marke Economy, IEEE Inernaional Conference on Roboics and Auomaion, May 22.