Martingale approach to optimal portfolio-consumption problems in Markov-modulated pure-jump models
Portfolio Management
2014-06-13 v1 Probability
Abstract
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.
Keywords
Cite
@article{arxiv.1406.3112,
title = {Martingale approach to optimal portfolio-consumption problems in Markov-modulated pure-jump models},
author = {Oscar Lopez and Rafael Serrano},
journal= {arXiv preprint arXiv:1406.3112},
year = {2014}
}