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Hedging of contingent claims written on non traded assets under Markov-modulated models. (English) Zbl 1343.60118
Summary: This paper studies the hedging problem of European contingent claims when the underlying asset is non-traded. We assume that the share prices of the assets are governed by Markov-modulated processes, that is, the market parameters switch over time according to a finite-state continuous-time Markov chain. Due to the presence of the Markov chain in the non-traded asset, the market which we consider is incomplete. We shall use the local risk minimization method to obtain an optimal hedging strategy in a closed-form for an investor. Finally, numerical illustrations of an optimal hedging strategy are given by Monte Carlo simulations.
MSC:
60J28 Applications of continuous-time Markov processes on discrete state spaces
60J27 Continuous-time Markov processes on discrete state spaces
91B70 Stochastic models in economics
91G80 Financial applications of other theories
91G60 Numerical methods (including Monte Carlo methods)
65C05 Monte Carlo methods
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