An anticipative Markov modulated market

Abstract

A Markovian modulation captures market trends and influences market coefficients accordingly. The various scenarios presented by the market are modeled as distinct states of a discrete-time Markov chain. In this paper we assume the existence of such modulation in a market and, as a novelty, propose that it can be anticipative with respect to the future of the Brownian motion driving the dynamics of the risky asset. Using techniques from the enlargement of filtrations, we solve an optimal portfolio utility problem in both complete and incomplete markets. Several examples of anticipative Markov chains are provided, for which we calculate the additional gains available to an investor with more accurate information.