Some possible applications of bivariate Markov processes

In this paper we propose a simple way to approximate a bivariate wealth process obtained by two portfolios. Moreover we analyze possible financial applications in portfolio theory, option pricing and risk management. More precisely, we approximate the evolution of a bivariate Markov process by using a proper Markov chain. As far as the applications are concerned, first we show how to use the forecasted joint distribution to evaluate the association between market stochastic bounds and future wealth in large scale portfolio problems. Secondly, we analyze its use in some classical risk management problems. Finally, we describe a methodology to price Asian options using a similar bivariate Markov process.