RISK‐MINIMIZING HEDGING STRATEGIES UNDER RESTRICTED INFORMATION

Abstract

We construct risk‐minimizing hedging strategies in the case where there are restrictions on the available information. the underlying price process is a d‐dimensional F‐martingale, and strategies φ= (ϑ, η) are constrained to have η G‐predictable and η G'‐adapted for filtrations η G C G’C F. We show that there exists a unique (ηG, G')‐risk‐minimizing strategy for every contingent claim H ε E 𝓎2 (𝓎T, P) and provide an explicit expression in terms of η G‐predictable dual projections. Previous results of Föllmer and Sondermann (1986) and Di Masi, Platen, and Runggaldier (1993) are recovered as special cases. Examples include a Black‐Scholes model with delayed information and a jump process model with discrete observations.