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A comparison of two quadratic approaches to hedging in incomplete markets. (English) Zbl 1032.91058

The valuation and hedging of derivatives in incomplete financial markets is a frequently studied problem in mathematical finance that still lacks of a commonly agreed uniformly superior method. The authors with their paper try to contribute to the discussion on this issue by comparing both theoretically and numerically the two main competing quadratic hedging approaches, the local risk-minimization and the mean-variance hedging in a class of stochastic volatility models. They explain the theory for both approaches in a general framework, they specialise to a Markovian situation, and then analyse in detail variants of two well-known stochastic volatility models, the Heston and Stein and Stein models. They also provide numerical results obtained mainly through the use of partial differential equations and simulation methods taking special care in order to check that the presented examples satisfy the required by the general related theory conditions.

MSC:

91B26 Auctions, bargaining, bidding and selling, and other market models
91B30 Risk theory, insurance (MSC2010)
91B70 Stochastic models in economics
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