Portfolio management in a stochastic factor model under the existence of private information

Abstract

In the present article, we study an optimal control problem for a general stochastic factor model under the existence of private information. More precisely, we consider a portfolio manager who has the possibility to invest part of her wealth in a financial market consisting of a risk-free asset and a risky one, whose coefficients depend on some external stochastic factor. Moreover, we assume that the manager, from the beginning of the trading interval, observes an information signal associated with the future evolution of the risky asset. This information is not clear but is subject to some observation noise. Within a very general framework, by resorting to a mixture of dynamic programming and initial enlargement of filtrations techniques, we characterize the optimal value function and the feedback control law, by solving an expected utility maximization problem under the enlarged information set of the economic agent. In the case of the exponential utility function and considering a specific form for the market parameters and the information signal, we provide closed form solutions for the optimal investment decision and the optimal value function. Additionally, by employing an Euler–Maruyama scheme followed by a Monte-Carlo approach, we numerically study the impact of the private information on the optimal investment strategy for this concrete example. The article has Supplementary Material, which provides the extension of our model to other classes of utility functions (logarithmic and power) and also presents the general case of multiple assets and factors.

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