  We study optimal investment strategies that maximize expected utility from
consumption and terminal wealth in a pure-jump asset price model with
Markov-modulated (regime switching) jump-size distributions. We give sufficient
conditions for existence of optimal policies and find closed-form expressions
for the optimal value function for agents with logarithmic and fractional power
(CRRA) utility in the case of two-state Markov chains. The main tools are
convex duality techniques, stochastic calculus for pure-jump processes and
explicit formulae for the moments of telegraph processes with Markov-modulated
random jumps.
