A Generalized Cameron–Martin Formula with Applications to Partially Observed Dynamic Portfolio Optimization
Gady Zohar
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Source: Crossref
Published: Oct 1, 2001
DOI: 10.1111/1467-9965.00125
Open original source ↗Source 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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