Unconstrained Hedging within a Regime-Switching Market Model

Abstract

We address a problem of unconstrained hedging within a regime-switching market model. The essence of the problem is as follows: a random variable B (called a contingent claim) is stipulated and an agent trades in a market over a fixed finite interval $t\in[0,\ T]$. The goal of hedging is to determine the least initial wealth (called the price of the contingent claim) such that, starting from this wealth, the agent can trade in such a way that, at close of trade $t=T$, the wealth of the agent is almost-surely greater than or equal to the contingent claim B (enabling the agent to “pay off” the contingent claim). The problem of hedging (constrained as well as unconstrained) has been addressed within the framework of Brownian motion market models (see [1] and [2]). Our goal is to study this problem for market models which also include regime-switching in the sense that the market parameters are adapted not only to the filtration of a given Brownian motion (as is the case in Brownian motion market models) but to the joint filtration of a Brownian motion together with a regime-switching Markov chain.