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We study optimal investment strategies that maximize expected utility fromconsumption and terminal wealth in a pure-jump asset price model withMarkov-modulated (regime switching) jump-size distributions. We give sufficientconditions for existence of optimal policies and find closed-form expressionsfor the optimal value function for agents with logarithmic and fractional power(CRRA) utility in the case of two-state Markov chains. The main tools areconvex duality techniques, stochastic calculus for pure-jump processes andexplicit formulae for the moments of telegraph processes with Markov-modulatedrandom jumps.

Martingale approach to optimal portfolio-consumption problems in Markov-modulated pure-jump models