Stanley R. Pliska  Ph.D., Stanford University, 1972 Professor of Finance  Department of Finance (2423 University Hall)  601 South Morgan Street; Chicago IL 60607-7124  Telephone, Messages, and Fax: 312-996-7170  srpliska (at) uic.edu  Paul Erdos number: 4  Kevin Bacon number: 2

Primary Activities and Miscellaneous Highlights (click here for my resume):

• Rothschild Visiting Professor, Isaac Newton Institute, Cambridge University, Spring 2005
• Organizer, Third World Congress, Bachelier Finance Society, Chicago, July 21-24, 2004
• Founder and Former Editor, Mathematical Finance
• Author: Introduction to Mathematical Finance: Discrete Time Models. Available from Blackwell Publishers (800-216-2522)
• Co-editor (with M.A.H.Dempster): Mathematics of Derivative Securities. Available now from Cambridge University Press.
• Former Executive Secretary and Council Member: Bachelier Finance Society
• Consultant: risk management and portfolio management

• FIN 516 Theory and Structure of Futures and Options Markets (Fall 2007)
• FIN 551 Financial Decision Making I (Fall 2007)
• FIN 594 Special Topics in Finance: International Futures Markets (Spring 2007)
• FIN 500 Introduction to Corporate Finance (Spring 1999)
• MBA 594 Corporate Risk Management (Spring 1999)
• MBA Spring 1998 module, Selected Topics in Finance
• FIN 416 Options and Futures Markets (Spring 2003)

Current Research:

• Risk Sensitive Portfolio Management and other Portfolio Optimization Problems
• Valuation of mortgages and mortgage backed securities
• Portfolio Management with Taxes and Transaction Costs
• Financial Planning: optimal life insurance purchase, consumption, and investment decisions

• Optimal Life Insurance Purchase, Consumption and Investment (with Jinchun Ye)
• This paper, which is based on part of Jinchun Ye's 2006 Ph.D. dissertation, was prepared for the 2006 Phelim Boyle Festkolloquium at the University of Waterloo and is an extension of "Optimal Life Insurance Purchase and Consumption/Investment under Uncertain Lifetime" (see below). Here, in addition to a riskless bank account, available for the purposes of investment is a risky security modeled as geometric Brownian motion. We use dynamic programming to analyze this problem and derive the optimal insurance, consumption and investment rules. Explicit solutions are found for the family of CRRA utilities, and the demand for life insurance is studied by examining our solutions and doing numerical experiments. Proofs and many technical details have been omitted, but they can be found in Jinchun Ye's dissertation as well as in a forthcoming paper.
• A Note on the Effects of Taxes and Transaction Costs on Optimal Investments (with Cristin Buescu and Abel Cadenillas) -- to appear in Mathematical Finance
• This paper considers a financial market consisting of two securities: a geometric Brownian motion stock and a riskless bank account. Whenever a transaction occurs that shifts funds from one security to the other, there is a fixed transaction cost, taxes must be paid on any profits, and a tax credit is received for any loss. Under the log utility criterion of maximizing the long-run asymptotic growth rate, the optimal strategy is developed, and two rather surprising conclusions emerge. It can be optimal to realize not only losses but also gains. Moreover, under certain circumstances the investor prefers a taxable over a tax-free market.

• Optimal Life Insurance Purchase and Consumption/Investment under Uncertain Lifetime (with Jinchun Ye) -- Journal of Banking and Finance 31/5 (May 2007) 1307-1319.
• In this paper, which is based on part of Jinchun Ye's 2006 Ph.D. dissertation, we consider optimal insurance purchase, consumption, and investment rules for a wage earner whose lifetime is random. The wage earner is endowed with an initial wealth, and he also receives an income continuously, but this may be terminated by the wage earner's premature death. This income is divided between consumption until death or retirement (whichever happens first), purchase of life insurance, and investment in a riskless bank account. The wage earner's objective is to maximize the expectation of the utility of consumption, the utility of the bequest if there is a premature death, and the utility of wealth at retirement if there is no premature death.  We use dynamic programming to analyze this problem and derive the optimal insurance, consumption and investment rules. Explicit solutions are found for the family of CRRA utilities, and the demand for life insurance is studied by examining our solutions and doing numerical experiments. This paper was prepared for a 2005 workshop at the University of Wisconsin in Milwaukee.

• Optimal Mortgage Refinancing with Endogenous Mortgage Rates: an Intensity Based, Equilibrium Approach
• This paper summarizes recent research on a new approach, namely, an equilibrium approach, to the valuation of fixed-rate mortgage contracts. Working in a discrete time setting with the mortgagor's prepayment behavior described by a suitable intensity process and with exogenous mortgage rates, the value of the contract is derived in an explicit form that can be interpreted as the principal balance plus the value of a certain swap. This leads to a nonlinear equation for what the mortgage rate must be in a competitive market, and thus mortgage rates are endogenous and depend upon the mortgagor's prepayment behavior. The complementary problem, where mortgage rates are exogenous and the mortgagor seeks the optimal refinancing strategy, is then solved via a Markov decision chain. Finally, the equilibrium problem, where the mortgagor is a representative agent in the economy who seeks the optimal refinancing strategy and where the mortgage rates are endogenous, is developed, solved, and analysed. Existence and uniqueness results, as well as a numerical example, are provided.

• Mortgage Valuation and Optimal Refinancing
• This is an abridged version of the above mortgage paper and has been published in Stochastic Finance, Proceedings of a 2004 conference in Lisbon, Portugal, edited by A. Shiryaev et al., published in 2006 by Springer.

• Optimal Investment Decisions for a Portfolio with a Rolling Horizon Bond and a Discount Bond (with T. Bielecki and J. Yong) -- International Journal of Theoretical and Applied Finance 8/7 (2005), 871-913.
• An optimal investment problem is considered for a continuous time market consisting of the usual bank account, a rolling horizon bond, and a discount bond whose maturity coincides with the investor's planning horizon. Two economic factors, namely, the short rate and the risk-free yield of some maturity, are modeled as Gaussian processes. For the problem of maximizing expected HARA utility of terminal wealth, the optimal portfolio is obtained through a Bellman equation. The results are noteworthy because the discount bond, which is the riskless asset for the investor, causes a degeneracy due to its zero volatility at the planning horizon. Indeed, this delicate matter is treated rigorously for what seems to be the first time, and it is shown that there exists an optimal, admissible (but unbounded) trading strategy.

• A 3-Factor Valuation Model for Mortgage-Backed Securities (MBS) (with T. Kariya and F. Ushiyama)
• This paper generalizes the one-factor MBS-pricing model proposed by Kariya and Kobayashi (2000) to a 3-factor model, describing prepayment behavior due to refinancing and house sales by incentive response functions. The valuation of an MBS is based on a discrete time, no-arbitrage framework, making an association between prepayment behavior and cash flow patterns. The structure and rationality of the model is demonstrated by valuing an MBS via Monte Carlo simulation and analysing the results. (Presented at the ASSA Meeting, Washington, DC, January 2003)
• Risk Sensitive Portfolio Management with Cox-Ingersoll-Ross Interest Rates: the HJB Equation (with T. Bielecki and S. Sheu) -- SIAM J. Control and Optimization 44/5 (2005), 1811-1843.
• This paper presents an application of risk sensitive control theory in financial decision making. The investor has an infinite horizon objective that can be interpreted as maximizing the portfolio's risk adjusted exponential growth rate. There are two assets, a stock and a bank account, and two underlying Brownian motions, so this model is incomplete. The novel feature here is that the interest rate for the bank account is governed by Cox-Ingersoll-Ross dynamics. This is significant for risk sensitive portfolio management because the factor process, unlike in the Gaussian and all other cases treated in the literature, cannot be negative (under appropriate parameterization).
• Continuous-Time Mean-Variance Portfolio Selection with Bankruptcy Prohibition (with T. Bielecki, H. Jin, and X.Y. Zhou) -- Mathematical Finance 15/2 (2005), 213-244.
• A continuous time mean-variance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time. The problem is completely solved using a decomposition approach. Specifically, a (constrained) variance minimizing problem is formulated and its feasibility is characterized. Then, after having solved a system of equations for two Lagrange multipliers, variance minimizing portfolios are derived as the replicating portfolios of some contingent claims, and the variance minimizing frontier is obtained. Finally, the efficient frontier is identified as an appropriate portion of the variance minimizing frontier, and all the efficient portfolios are found. In the special case where the market coefficients are deterministic, efficient portfolios are explicitly expressed as feedback of the current wealth, and the efficient frontier is represented by parameterized equations. Our results indicate that the efficient policy for a mean-variance investor is simply to purchase a certain kind of option which, in the case of a single stock, resembles, but is not identical to, a call option.
• Risk Sensitive Portfolio Optimization with Transaction Costs (with T. Bielecki, J.P. Chancelier, and A. Sulem) -- Computational Finance Vol. 8, No. 1 (September 2004), 39-63.
• We develop methods of risk sensitive impulsive control theory in order to solve an optimal asset allocation problem with transaction costs and a stochastic interest rate. The optimal trading strategy and the risk-sensitized expected exponential growth rate of the investor's portfolio are characterized in terms of a nonlinear quasi-variational inequality. This problem can then be interpreted as the ergodic Isaac-Hamilton-Jacobi equation associated with a min-max problem. We use a numerical method based on an extended two-stage policy iteration algorithm for min-max problems and provide numerical results for the case of two assets and one factor that is a Vasicek interest rate.

• Optimal Tracking for Asset Allocation with Fixed and Proportional Transaction Costs (with K. Suzuki) -- Quantitative Finance Vol. 4, Issue 2 (April 2004), 233-243.
• This paper considers the optimal trading strategy for an investor who is trying to minimize both fixed and proportional trading costs while simultaneously minimizing the tracking error with respect to a specified, target asset mix. Impulse control theory in a continuous-time setting is used, leading to optimal solutions via a quasi-variational inequality. An explicit solution is derived for a two-asset case (e.g., a bond fund versus a stock fund); a sensitivity analysis examines how the optimal trading strategy depends upon individual input parameters. In addition, some theory for one-dimensional diffusion processes is used to derive analytical expressions for various measures of performance associated with a fixed trading strategy.
• Risk Sensitive Intertemporal CAPM, With Application to Fixed Income Management (with T. Bielecki) -- IEEE Transactions on Automatic Control (special issue on stochastic contro methods in financial engineering) Vol. 49, No. 3 (March 2004), 420-432.
• This paper presents an application of risk sensitive control theory in financial decision making. A variation of Merton's continuous-time intertemporal capital asset pricing model is developed where the infinite horizon objective is to maximize the portfolio's risk adjusted growth rate. The resulting model is tractable and thus provides economic insight about optimal trading strategies as well as the fact that the strategy of 100% cash is not necessarily the least risky one. For fixed income applications we utilize the concept of rolling-horizon bonds, which are stochastic process models of certain mutual funds of zero coupon bonds. We show by numerical example that the optimal proportion of one's wealth to hold in an asset is given by a simple affine function of economic factors such as interest rates of various maturities.

• Option Valuation with Co-Integrated Asset Prices (with Jin-Chuan Duan) -- J. Economic Dynamics & Control, Vol. 28, Issue 4 (January 2004), 727-754.
• Many financial data series are found to be co-integrated. The implications of co-integration on option valuation are studied in this article, as we develop the option valuation theory for co-integrated price systems. We also examine the diffusion limit of the system and numerically analyze the co-integration effect on spread options. The consideration of co-integration is found to yield an option pricing theory that depends on co-integration premiums if the volatility is stochastic. Our numerical results suggest that co-integration can substantially alter the value of the spread option.
• Economic Properties of the Risk Sensitive Criterion for Portfolio Management -- The Review of Accounting and Finance, Vol. 2, No. 2 (2003), 3-17.
• The idea of using stochastic control methods for theoretical studies of portfolio managment has been standard, with maximum expected utility criteria commonly being used. But in recent years a new kind of criterion, the risk sensitive criterion, has emerged from the control theory literature and been applied to portfolio management. This paper studies various economic properties of this criterion for portfolio management, thereby providing justification for its theoretical and practical use. In particular, it is shown that the risk sensitive criterion amounts to maximizing a portfolio's risk adjusted growth rate. In other words, it is essentially the same as what is commonly done in practice: find the best trade-off between a portfolio's average return and its average volatility.
• Option Pricing for Co-Integrated Assets (with Jin-Chuan Duan) -- Advances in Finance and Stochastics, edited by K. Sandmann and P. Schoenbucher, Springer, 2002,  85-100.
• This is a preliminary, proceedings version of  "Option Valuation with Co-Integrated Asset Prices" (see above).

• Risk Sensitive Asset Management with Constrained Trading Strategies (with T. Bielecki and D. Hernandez-Hernandez) -- Recent Developments in Mathematical Finance, edited by J. Yong, World Scientific, Singapore, 2002, 127-138.
• This paper investigates a variation of the model in "Risk Sensitive Intertemporal CAPM, with Applications to Fixed Income Management" where there are constraints on the trading strategies. A discrete time, controlled Markov chain approximation is used, and the resulting optimization problem is solved with the method of successive approximations. It is shown that this procedure is effective for cases where there are only a few factors.

• Risk Sensitive Control with Applications to Fixed Income Portfolio Management (with T. Bielecki) -- Proceedings of the European Congress of Mathematics, Barcelona, July 10-145, 2000, edited by C. Casacuberta, R.M. Miro-Roig, J. Verdera, and S. Xambo, Birkhaeuser, Basel, Switzerland.
• This is a short, preliminary version of Risk Sensitive Intertemporal CAPM, With Application to Fixed Income Management (see above).

• Risk Sensitive Asset Management: Two Empirical Examples (with T. Bielecki, A. Harris, and J. Li) -- Proceedings of the October 2000 Conference on Mathematical Finance in Konstanz, Germany (2001), edited by M. Kohlmann and S. Tang, Birkhaeuser, Basel, Switzerland, 99-110.
• This paper is concerned with applications of risk sensitive control theory in financial decision making. In earlier work a variation of Merton's continuous-time, intertemporal capital asset pricing model was developed where the infinite horizon objective is to maximize the portfolio's risk adjusted growth rate. Here this model is illustrated by applying it to two portfolio managment problems based upon historical data. In the first there are four assets (a bank account, the Dow Jones Industrials index, the S&P 500 index, and the NASDAQ index) and two stochastic economic factors (the short interest rate for the bank account and a long term U.S. Treasury yield). In the second example there are six economic factors, namely, U.S. Treasury yields of various maturities; in addition to the usual bank account, the other assets are rolling horizon bonds corresponding to the factors. These examples demonstrate that the risk sensitive asset management model is tractable and provides economic insight as well as useful results, although the optimal strategies sometimes involve high levels of leverage.

• Risk Sensitive Control of Finite State Markov Chains in Discrete Time, with Applications to Portfolio Management (with T. Bielecki and D. Hernandez-Hernandez) Mathematical Methods of Operations Research 50 (1999) 167-188.
• In this paper we extend standard dynamic programming results for the risk sensitive optimal control of discrete time Markov chains to a new class of models. The state space is only finite, but now the assumptions about the Markov transition matrix are much less restrictive. Our results are then applied to the financial problem of managing a portfolio of assets which are affected by Markovian microeconomic and macroeconomic factors and where the investor seeks to maximize the portfolio's risk adjusted growth rate.

• Risk Sensitive Dynamic Asset Allocation (with T. Bielecki) In Asset & Liability Management: A Synthesis of New Methodologies, published by RISK Books, 1998.
• This paper is largely an applied version of Risk Sensitive Asset Allocation (see below). In addition to a presentation of the Vasicek example and some empirical results, this paper explains why rolling Markowitz trading strategies are often inferior to more sophisticated dynamic trading strategies.

• Risk Sensitive Asset Management with Transaction Costs (with T. Bielecki) Finance & Stochastics 4 (2000) 1-33.
• This paper develops a continuous time risk-sensitive portfolio optimization model with a general transaction cost structure and where the assets are explicitly affected by underlying economic factors such as dividend yields, a firm's return on equity, interest rates, and unemployment rates. In particular, the security prices and factors follow diffusion processes, and both the drift and diffusion coefficients for the securities are explicit functions of the factor levels. We develop methods of risk sensitive impulsive control theory in order to maximize an infinite horizon objective that is natural and features the long run expected growth rate, the asymptotic variance, and a single risk aversion parameter. It is shown that the optimal trading strategy has a simple characterization in terms of the security prices and factor levels. Moreover, the optimal strategy can be computed by solving a risk sensitive quasi variational inequality. The risk-null (i.e., Kelly criterion) case is also studied, and the various results are related to the recent work by Morton and Pliska.

• Risk Sensitive Asset Allocation (with T. Bielecki and M. Sherris) -- J. Economic Dynamics & Control 24 (2000), 1145-1177.
• This paper develops a continuous time modeling approach for making optimal asset allocation decisions. Macroeconomic and financial factors are explicitly modeled as Gaussian stochastic processes which directly affect the mean returns of the assets. We employ methods of risk sensitive control theory, as explained in a companion paper "Risk Sensitive Dynamic Asset Management." Explicit formulas can be obtained, as is illustrated here by an example where the only factor is a Vasicek-type interest rate and where there are two assets: cash and a stock index. The methods are futher illustrated by backtest studies with two data sets: U.S. data with two assets and up to three factors, and Australian data with three assets and up to three factors.

• Risk Sensitive Dynamic Asset Management (with T.Bielecki) -- J. Appl. Math. & Optimization 37 (1999), 337-360.
• This paper develops a continuous time portfolio optimization model where the mean returns of assets are explicitly affected by underlying economic factors (such as dividend yields and interest rates) which are modeled as Gaussian processes. We employ methods of risk sensitive control theory, thereby using an infinite horizon objective that is natural and features the exponential growth rate, the asymptotic variance, and a single risk aversion parameter. Even with constraints on the admissible trading strategies, it is shown that the optimal trading strategy has a simple characterization in terms of the factor levels and can be computed with quadratic programming. The optimal objective value comes from the solution of a partial differential equation.
• Optimal Trading of a Security When There Are Taxes and Transaction Costs (with A.Cadenillas) -- Finance & Stochastics 2 (1999), 137-165.
• We revisit the problem of investing in securities in order to maximize the after-tax rate of return. We consider a single stock modelled as geometric Brownian motion along with the objective of maximizing the long-run growth rate of after-tax wealth. We show that is is optimal not only to cut short the losses, but also the profits, even though there is no distinction between short and long term rates. Moreover, it may be preferable to invest in a taxable world than in a non-taxable one. These surprising results may be due to the possibility of using the tax system to reduce after-tax volatility.

• "Portfolio management with transaction costs" (with C.Atkinson and P.Wilmott), Phil. Trans. R. Soc. London A, (1997).
• "Optimal portfolio management with fixed transaction costs" (with A.J.Morton), Mathematical Finance 5 (1995), 337-356.
• "On a free boundary problem that arises in portfolio management" (with M.J.P.Selby), Phil. Trans. R. Soc. London A, Vol. 347 (1994), 555-561.
• "Optimal portfolios with asymptotic criteria" (with H.Konno and K.Suzuki), Annals of Operations Research 45 (1993), 187-204.
• "The Effects of Regulations on Trading Activity and Return Volatility in Futures Markets," (with C.T. Shalen), The Journal of Futures Markets, 1991.
• "Kalman Filter Estimation for Valuing Nontrading Securities, with Applications to the MMI Cash-Futures Spread on October 19 and 20, 1987, (with G. Bassett & V. France), The Review of Quantitative Finance and Accounting, 1991, pp. 135-151.
• "On the Fundamental Theorem of Asset Pricing with an Infinite State Space," (with K. Back), Journal of Mathematical Economics, 1991, pp. 1-18.
• "The MMI Cash-Futures Spread on October 19, 1987, (with G. Bassett & V. France), The Review of Futures Markets, 1989, pp. 118-138.
• "Martingales and Stochastic Integrals in the Theory of Continuous Trading," (with J.M. Harrison), Stochastic Processes and Their Applications, 1981, pp. 215-260.

• Prudential Distinguished Visiting Fellow, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, January-June, 1995.
• Head, Department of Finance, UIC, 1988-1991.
• Distinguished Visiting Fellow, London School of Economics, Suntory Toyota International Centre for Economics and Relation Disciplines, London, England, March-July, 1992.
• Yamaichi Endowed Chair, Visiting Professor of Finance, The University of Tsukuba, Tokyo, Japan, August 1991-February 1992.
• Consultant, Aon Financial Advisors, 1998-2000.
• Consultant, Geldermann, Inc., Chicago, IL, 1991.
• Research Grant, "The MMI Cash-Futures Spread during the October 1987 Stock Market Crash," 1988-1989.
• Co-Principal Investigator, Chicago Board of Trade Educational and Research Foundation
• Consultant, Hines VA Hospital, Maywood, IL, 1986.
• Consultant, Sears, Roebuck and Company, Chicago, IL, 1982.
• Consultant, Standard Oil Company (Indiana), Chicago, IL, 1978.