Risk sensitive asset management with transaction costs

Abstract. This paper develops a continuous time risk-sensitive portfolio optimization model with a general transaction cost structure and where the individual securities or asset categories are explicitly affected by underlying economic factors. The security prices and factors follow diffusion processes with the drift and diffusion coefficients for the securities being 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. The optimal trading strategy has a simple characterization in terms of the security prices and the factor levels. Moreover, it can be computed by solving a {\it risk sensitive quasi-variational inequality}. The Kelly criterion case is also studied, and the various results are related to the recent work by Morton and Pliska.

[1]  Robert J. Elliott,et al.  Stochastic calculus and applications , 1984, IEEE Transactions on Automatic Control.

[2]  Ioannis Karatzas,et al.  Lectures on the Mathematics of Finance , 1996 .

[3]  S. Pliska,et al.  Risk-Sensitive Dynamic Asset Management , 1999 .

[4]  S. Pliska,et al.  Risk sensitive asset allocation , 2000 .

[5]  M. Robin.  On Some Impulse Control Problems with Long Run Average Cost , 1981 .

[6]  A. Borodin,et al.  Handbook of Brownian Motion - Facts and Formulae , 1996 .

[7]  A. R. Norman,et al.  Portfolio Selection with Transaction Costs , 1990, Math. Oper. Res..

[8]  M. Schäl.  A selection theorem for optimization problems , 1974 .

[9]  R. C. Merton,et al.  AN INTERTEMPORAL CAPITAL ASSET PRICING MODEL , 1973 .

[10]  W. Fleming,et al.  Controlled Markov processes and viscosity solutions , 1992 .

[11]  A. Timmermann,et al.  Predictability of Stock Returns: Robustness and Economic Significance , 1995 .

[12]  S. Pliska,et al.  OPTIMAL PORTFOLIO MANAGEMENT WITH FIXED TRANSACTION COSTS , 1995 .

[13]  Stanley R. Pliska,et al.  On a free boundary problem that arises in portfolio management , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[14]  Ł. Stettner.  On ergodic stopping and impulsive control problems for nonuniformly ergodic Markov processes , 1989 .

[15]  Kevin J. Hastings.  Impulse control of portfolios with jumps and transaction costs , 1992 .

[16]  Ralf Korn,et al.  Portfolio optimisation with strictly positive transaction costs and impulse control , 1998, Finance Stochastics.

[17]  N. Krylov.  Controlled Diffusion Processes , 1980 .

[18]  P. Whittle.  Risk-Sensitive Optimal Control , 1990 .

[19]  Wendell H. Fleming.  Optimal investment models and risk sensitive stochastic control , 1995 .

[20]  R. C. Merton,et al.  Optimum Consumption and Portfolio Rules in a Continuous-Time Model* , 1975 .

[21]  Jerome F. Eastham,et al.  Optimal Impulse Control of Portfolios , 1988, Math. Oper. Res..

[22]  Alain Bensoussan,et al.  Impulse Control and Quasi-Variational Inequalities , 1984 .

[23]  Michael J. Klass,et al.  A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees , 1988, Math. Oper. Res..

[24]  P. Wilmott,et al.  Portfolio Management With Transaction Costs: An Asymptotic Analysis Of The Morton And Pliska Model , 1995 .

[25]  Eduardo S. Schwartz,et al.  Strategic asset allocation , 1997 .

[26]  A. Bensoussan.  Stochastic control by functional analysis methods , 1982 .

[27]  H. Soner,et al.  Optimal Investment and Consumption with Transaction Costs , 1994 .

[28]  Ioannis Karatzas,et al.  Brownian Motion and Stochastic Calculus , 1987 .

[29]  Jakša Cvitanić,et al.  HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH12 , 1996 .