Hedging Under Generalized Good-Deal Bounds and Model Uncertainty

Abstract

We study a notion of good-deal hedging, that corresponds to good-deal valuation and is described by a uniform supermartingale property for the tracking errors of hedging strategies. For generalized good-deal constraints, defined in terms of correspondences for the Girsanov kernels of pricing measures, constructive results on good-deal hedges and valuations are derived from backward stochastic differential equations, including new examples with explicit formulas. Under model uncertainty about the market prices of risk of hedging assets, a robust approach leads to a reduction or even elimination of a speculative component in good-deal hedging, which is shown to be equivalent to a global risk-minimization in the sense of Föllmer and Sondermann (1986) if uncertainty is sufficiently large.

Keywords: Incomplete markets, good-deal bounds, model uncertainty, good-deal hedging, multiple priors, backward stochastic differential equations

JEL Classification: C61, D80, G11, G13, G17