Optimal portfolio selection with threshold in stochastic market

This paper considers a continuous-time optimal portfolio problem, where the price processes of assets depend on the state of the stochastic market, which is assumed to follow a diffusion process. And trading in the risky asset is stopped if the market state hits a predefined threshold. The problem is formulated as a utility maximization with random horizon. Using the techniques of dynamic programming and Feynman-Kac representation theorem, we obtain a stochastic representation of optimal portfolio. Furthermore, in some special case, the closed-form of optimal portfolio is derived. Finally, we present computational results that show the differentiation between this proposed model and classical Merton model.