Optimal investment-consumption problem with discontinuous prices and random horizon

This paper investigates an international optimal investmentCconsumption problem under a random time horizon. The investor may allocate wealth between a domestic bond and an international real project with production output, whose price may exhibit discontinuities. The model incorporates the effects of taxation and exchange rate dynamics, where the exchange rate follows a stochastic differential equation with jump-diffusion. The investor's objective is to maximize the utility of consumption and terminal wealth over an uncertain investment horizon. It is worth noting that, under our framework, the exit time is not assumed to be a stopping time. In particular, for the case of constant relative risk aversion (CRRA), we derive the optimal investment and consumption strategies by applying the separation method to solve the associated HamiltonCJacobiCBellman (HJB) equation. Moreover, several numerical examples are provided to illustrate the practical applicability of the proposed results.