Hedging under generalized good-deal bounds and model uncertainty

TL;DR

This paper explores robust good-deal hedging under model uncertainty, showing how it reduces speculative risk and connects to global risk minimization, with explicit solutions derived from backward stochastic differential equations.

Contribution

It introduces a robust framework for good-deal hedging under model uncertainty, linking it to global risk minimization and providing explicit solutions via backward stochastic differential equations.

Findings

Model uncertainty reduces speculative components in hedging.

Robust hedging aligns with global risk minimization under high uncertainty.

Explicit solutions for hedging and valuation are derived from BSDEs.

Abstract

We study a notion of good-deal hedging, that corresponds to good-deal valuation for generalized good-deal constraints. 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 F\"ollmer and Sondermann (1986) if uncertainty is sufficiently large. Constructive results on hedges and valuations are derived from backward stochastic differential equations, including new examples with explicit formulas.