Optimal investment and consumption with event risk

This paper concerns the problem of optimal investment and consumption with power utility when there is event risk. Events are modelled by transitions in a finite state Markov chain, but unlike traditional regime switching models, changes in regime (i.e. events) may be accompanied by jumps in the asset price at the instant of transition, where the distribution of the jump sizes are conditional on the regime before and after the transition. This enables us to model a situation where a transition from a ‘good’ regime to a ‘bad’ one (for instance) is likely to be accompanied by a downward jump in the price, while transitions from a ‘bad’ regime to a ‘good’ one is likely to be accompanied by an upward jump. Expressions for the optimal investment portfolio and consumption policy are obtained using stochastic control methods. It is shown that the event risk models we consider have optimal solutions that are significantly different from those associated with traditional regime switching models where regime transitions are typically not accompanied by jumps. Key words– Event risk, regime switching, defaultable bonds, jump processes, optimal investment and consumption, stochastic control