Wendell H. Fleming and Shuenn-Jyi Sheu
An optimal investment policy model for the long term growth of
expected utility of wealth is considered. The utility function is HARA with
exponent $-\infty < \gamma < 1$. The problem can be reformulated as an
infinite time horizon, risk sensitive control problem. Then the dynamic
programming equations for different HARA exponents and different policy
constraints are studied. We obtain some estimates for the solution of each
equation. This can be used to derive an optimal policy with some interesting
properties.
Primary Subjects: 90A09, 93E20
Secondary Subjects: 60H30, 90A19
References
Bielecki, T. R. and Pliska, S. R. (1997). Risk sensitive dy namic asset management. Preprint.
Cvitanic, J. and Karatzas, I. (1995). On portfolio optimization under drawdown constraints. IMA Vol. Math. Appl. 65 35-45. Springer, New York.
Fleming, W. H. (1995). Optimal investment models and risk-sensitive stochastic control. IMA Vol. Math. Appl. 65 75-88. Springer, New York.
Fleming, W. H., Grossman, S. G., Vila, J.-L. and Zariphopoulou, T. (1990). Optimal portfolio rebalancing with transaction costs. Preprint.
Fleming, W. H. and McEneaney, W. M. (1995). Risk-sensitive control on an infinite time horizon. SIAM J. Control Optim. 33 1881-1915.
Fleming, W. H. and Rishel, R. W. (1975). Deterministic and Stochastic Optimal Control. Springer, New York.
Fleming, W. H. and Soner, H. M. (1992). Controlled Markov Processes and Viscosity Solutions. Springer, New York.
Kaise, H. and Nagai, H. (1998). Bellman-Issacs equations of ergodic ty pe related to risk-sensitive control and their singular limits. Asy mptotic Anal. 16 347-362.
Khasminskii, R. Z. (1980). Stochastic Stability of Differential Equations. Sijhoff and Noordhoff.
Konno, H., Pliska, S. R. and Suzuki, R. I. (1993). Optimal portfolios with asy mptotic criteria, Ann. Oper. Res. 45 187-204.
Liptser, R. S. and Shiry ayev, A. N. (1977). Statistics of Random Processes I. Springer, New York.
Platen, E. (1996). Explaining interest rate dy namics. Financial Math. Research Report FMRR 001-96, Australian National Univ.
Platen, E. and Rebolledo, R. (1996). Principles for modelling financial markets, J. Appl. Probab. 33 601-603.
Reed, M. and Simon, B. (1978). Methods of Modern Mathematics physics IV. Academic Press, New York.
Taksar, M., Klass, M. and Assaf, D. (1988). Diffusion model for optimal portfolio selection in presence of brokerage fees. Math. Oper. Res. 13 277-294.
