| 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. |
