Title: Optimal portfolio selection in an Itô-Markov additive market,
Abstract: We study a portfolio selection problem in a continuous-time Itô-Markov
additive market with prices of financial assets described by Markov additive
processes which combine Lévy processes and regime switching models. Thus the
model takes into account two sources of risk: the jump diffusion risk and the
regime switching risk. For this reason the market is incomplete. We complete
the market by enlarging it with the use of a set of Markovian jump securities,
Markovian power-jump securities and impulse regime switching securities.
Moreover, we give conditions under which the market is
asymptotic-arbitrage-free. We solve the portfolio selection problem in the
Itô-Markov additive market for the power utility and the logarithmic utility.