Premium
RISK‐MINIMIZING HEDGING STRATEGIES UNDER RESTRICTED INFORMATION
Author(s) -
Schweizer Martin
Publication year - 1994
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.1994.tb00062.x
Subject(s) - martingale (probability theory) , mathematical economics , dual (grammatical number) , econometrics , expression (computer science) , economics , mathematics , computer science , actuarial science , mathematical optimization , art , literature , programming language
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 2 ( T , 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.