Construction of Mean-Self-Financing Strategies for European Options under Regime-Switching

Abstract

The paper focuses on the problem of pricing and hedging a European contingent claim for an incomplete market model, in which evolution of price processes for a saving account and stocks depends on an observable Markov chain. The pricing function is evaluated using the martingale approach. The equivalent martingale measure is introduced in such a way that the Markov chain remains the historical one. Due to the Markovian structure of the considered model, the pricing function satisfies the Cauchy problem for a system of linear parabolic partial differential equations. It is shown that any European contingent claim is attainable using a generalized replicating strategy which is self-financing in mean. For such a strategy, apart from the initial endowment and trading, some additional funds are required both stepwise at the jump moments of the Markov chain and continuously between the jump moments. The connection of the considered pricing and hedging problems with partial differential equations is very useful ...