We find the variance-optimal equivalent martingale measure when multivariate assets are modeled by a regime-switching geometric Brownian motion, and the regimes are represented by a homogeneous continuous time Markov chain. Under this new measure, the Markov chain driving the regimes is no...

In this article we find the optimal solution of the hedging problem in discrete time by minimizing the mean square hedging error, when the underlying assets are multidimensional, extending the results of Schweizer (1995). We also find explicit expressions for the optimal hedging problem in...

Sequential Monte Carlo (SMC) methods have successfully been used in many applications in engineering, statistics and physics. However, these are seldom used in financial option pricing literature and practice. This paper presents SMC method for pricing barrier options with continuous and...

In this paper, we consider an investor who plays in a market that involves a risky asset whose instantaneous rate of return changes at unknown random times. This return rate is assumed to follow the law of a Compound Poisson Process. We construct optimal mathematical strategies in this context...