Martingale approach to optimal portfolio-consumption problems in Markov-modulated pure-jump models
"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. Copyright © Taylor and Francis Group, LLC."
Calculations ; Stochastic systems ; Telegraph ; Markov-modulated ; Martingale method ; Optimal investment consumption ; Regime switching ; Utility maximizations ; Markov processes ; Jump-telegraph model ; Markov-modulated ; Martingale method ; Optimal investment-consumption ; Pure jump model ; Regime switching ; Utility maximization ;
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