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

Gady Zohar

Mathematical Finance, 2001, vol. 11, issue 4, 475-494

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.

Date: 2001
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