Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process

ABSTRACT

Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton–Jacobi–Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.

KEYWORDS:

• Exchange rate
• jump-diffussion process
• mean-variance criterion
• stochastic HJB equation
• safety-first criterion