ISSN:
1432-1122
Keywords:
Key words: Hedging, incomplete markets, dynamic programming, hedging numéraire, variance-optimal martingale measure JEL classification: G11, G12. Mathematics Subject Classification (1991): 90A09, 60H30, 90C39.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Economics
Notes:
Abstract. We consider the mean-variance hedging problem when asset prices follow Itô processes in an incomplete market framework. The hedging numéraire and the variance-optimal martingale measure appear to be a key tool for characterizing the optimal hedging strategy (see Gouriéroux et al. 1996; Rheinländer and Schweizer 1996). In this paper, we study the hedging numéraire $\tilde a$ and the variance-optimal martingale measure $\tilde P$ using dynamic programming methods. We obtain new explicit characterizations of $\tilde a$ and $\tilde P$ in terms of the value function of a suitable stochastic control problem. We provide several examples illustrating our results. In particular, for stochastic volatility models, we derive an explicit form of this value function and then of the hedging numéraire and the variance-optimal martingale measure. This provides then explicit computations of optimal hedging strategies for the mean-variance hedging problem in usual stochastic volatility models.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s007800050053
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