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 the authors 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 opitmal portfolio and the corresponding expected path-dependent utility. Finally, they provide a criterion to choose ‘buy and hold’ or ‘buy and sell’ strategies.