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A Generalized Cameron–Martin Formula with Applications to Partially Observed Dynamic Portfolio Optimization
Author(s) -
Zohar Gady
Publication year - 2001
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.00125
Subject(s) - martingale (probability theory) , mathematics , laplace transform , bellman equation , mathematical optimization , portfolio , computation , dynamic programming , generalization , bayesian probability , mathematical economics , economics , mathematical analysis , algorithm , statistics , financial economics
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.