Backward Stochastic Differential Equations with Continuous Coefficients in a Markov Chain Model and with Applications to European Options

Abstract

In this paper we discuss backward stochastic differential equations with Markov chain noise, having continuous drivers. We obtain the existence of a solution which is possibly not unique. Moreover, we show there is a minimal solution for this kind of equation and derive the corresponding comparison result. This is applied to pricing of European options in a market with Markov chain noise.