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A Generalized Cameron–Martin Formula with Applications to Partially Observed Dynamic Portfolio Optimization

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  • Gady Zohar

Abstract

The optimal dynamic allocation problem for a Bayesian investor is addressed when the stock's drift—modeled as a linear mean‐reverting diffusion—is not observed directly but only via the measurement process. Adopting a martingale approach, an appropriate generalization of the Cameron–Martin (1945) formula then enables computation of both the optimal dynamic allocation and the value function for a general utility function, in terms of an inverse Laplace transform of an explicit expression. Moreover, closed‐form formulas are provided in the case of power utility.

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  • Gady Zohar, 2001. "A Generalized Cameron–Martin Formula with Applications to Partially Observed Dynamic Portfolio Optimization," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 475-494, October.
    • Handle: RePEc:bla:mathfi:v:11:y:2001:i:4:p:475-494
    DOI: 10.1111/1467-9965.00125
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    Cited by:

    1. Zongxia Liang & Qi Ye, 2024. "Optimal information acquisition for eliminating estimation risk," Papers 2405.09339, arXiv.org.
    2. Nikolai Dokuchaev, 2015. "Optimal portfolio with unobservable market parameters and certainty equivalence principle," Papers 1502.02352, arXiv.org.
    3. Herve Roche, 2004. "Optimum Consumption and Portfolio Allocations under Incomplete Information," Econometric Society 2004 Latin American Meetings 79, Econometric Society.
    4. Brendle, Simon, 2006. "Portfolio selection under incomplete information," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 701-723, May.

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