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Exponential Utility Maximization under Partial Information

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  • Michael Mania
  • Marina Santacroce

Abstract

We consider the exponential utility maximization problem under partial information. The underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is available. We show that this problem is equivalent to a new exponential optimization problem, which is formulated in terms of observable processes. We prove that the value process of the reduced problem is the unique solution of a backward stochastic differential equation (BSDE), which characterizes the optimal strategy. We examine two particular cases of diffusion market models, for which an explicit solution has been provided. Finally, we study the issue of suffciency of partial information.

Suggested Citation

  • Michael Mania & Marina Santacroce, 2008. "Exponential Utility Maximization under Partial Information," ICER Working Papers - Applied Mathematics Series 24-2008, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpmath:24-2008
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Backward stochastic differential equation; semimartingale market model; exponential utility maximization problem; partial information; suffcient filtration.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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