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Risk-sensitive portfolio optimization with full and partial information. (English) Zbl 1068.60086
Kunita, Hiroshi (ed.) et al., Stochastic analysis and related topics in Kyoto. In honour of Kiyoshi ItĂ´. Lectures given at the conference, Kyoto, Japan, September 4–7, 2002. Tokyo: Mathematical Society of Japan (ISBN 4-931469-26-4/hbk). Advanced Studies in Pure Mathematics 41, 257-278 (2004).
An application of risk-sensitive control to portfolio optimization problems for a general factor model, which is considered as a variation of Merton’s intemporal capital asset pricing model, is discussed. In the model considered in the paper the instantaneous mean returns as well as volatilities of the security price processes are affected by economic factors and the security prices. The economic factors are assumed to satisfy stochastic differential equations whose coefficients depend on the security prices as well as themselves. In such general incomplete market models under Markovian setting, the construction of optimal strategies for risk-sensitive portfolio optimization problems on a finite time horizon is considered. The Bellman equations of parabolic type corresponding to the optimization problems are studied. Through the analysis of the Bellman equations, the optimal strategies from the solution of the equation are constructed. The corresponding problem with partial information is discussed. A necessary condition for the optimality using backward stochastic differential equations is also obtained.
For the entire collection see [Zbl 1050.60002].

60H30 Applications of stochastic analysis (to PDEs, etc.)
91G10 Portfolio theory
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35K20 Initial-boundary value problems for second-order parabolic equations