Before revision:  We give sufficient conditions for existence of optimal policies and find closed-form solutions for the optimal value function in the case of pure-jump models with jump-size distributions modulated by a two-state Markov chain and agents with logarithmic and fractional power utility .
After revision:  We give sufficient conditions for existence of optimal policies for agents with logarithmic and CRRA power utility. We find closed-form solutions for the optimal value function in the case of pure-jump models with jump-size distributions modulated by a two-state Markov chain and agents with logarithmic and fractional power utility .