A note on portfolio optimization with path-dependent utility

This paper considers the portfolio selection with preferences depending on the history of the wealth process. The maximization problem of the expected terminal utility consisting of the combination of two kinds of preferences is discussed in a continuous trading setting. Especially we focus on the relationship between the portfolio risk and the goal seeking behavior of the financial agent. The numerical example shows how the risk sensitivity affects the optimal portfolio and the corresponding expected path-dependent utility. Finally, we provide a criterion to choose buy and hold or buy and sell strategies.