In this paper, we consider the consumption and investment problem with random horizon in a Batch Markov Arrival Process (BMAP) model. The investor invests her wealth in a financial market consisting of a risk-free asset and a risky asset. The price processes of the riskless asset and the risky...

This paper considers a Markov-modulated jump-diffusion risk model with randomized observation periods and threshold dividend. A second order integro-differential system of equations that characterizes the expected discounted dividend payments is obtained. As a closed-form solution does not...