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Mean variance hedging in a general jump model. (English) Zbl 1229.91314

Summary: We consider the mean-variance hedging of a contingent claim \(H\) when the discounted price process \(S\) is an \(\mathbb R^d\)-valued quasi-left continuous semimartingale with bounded jumps. We relate the variance-optimal martingale measure (VOMM) to a backward semimartingale equation (BSE) and show that the VOMM is equivalent to the original measure \(P\) if and only if the BSE has a solution. For a general contingent claim, we derive an explicit solution of the optimal strategy and the optimal cost of the mean-variance hedging by means of another BSE and an appropriate predictable process \(\delta \)

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60H30 Applications of stochastic analysis (to PDEs, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G44 Martingales with continuous parameter
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