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Risk-Minimizing Hedging Strategies Under Restricted Information

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  • Martin Schweizer
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    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 &phis;= (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 𝓎-super-2 (𝓎 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. Copyright 1994 Blackwell Publishers.

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 4 (1994)
    Issue (Month): 4 ()
    Pages: 327-342

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    Handle: RePEc:bla:mathfi:v:4:y:1994:i:4:p:327-342

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    Cited by:
    1. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2013. "Local risk-minimization under restricted information to asset prices," Papers 1312.4385, arXiv.org.
    2. Covello, D. & Santacroce, M., 2010. "Power utility maximization under partial information: Some convergence results," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 2016-2036, September.
    3. M. Mania & R. Tevzadze & T. Toronjadze, 2007. "Mean-variance Hedging Under Partial Information," Papers math/0703424, arXiv.org.
    4. Mercurio, Fabio, 2001. "Claim pricing and hedging under market incompleteness and "mean-variance" preferences," European Journal of Operational Research, Elsevier, vol. 133(3), pages 635-652, September.
    5. Damiano Brigo & Bernard Hanzon, 2008. "On three filtering problems arising in mathematical finance," Papers 0812.4050, arXiv.org.
    6. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2013. "A Benchmark Approach to Risk-Minimization under Partial Information," Papers 1307.6036, arXiv.org.
    7. Damiano Brigo & Fabio Mercurio, 2008. "Discrete Time vs Continuous Time Stock-price Dynamics and implications for Option Pricing," Papers 0812.4010, arXiv.org.
    8. Romuald Momeya & Zied Salah, 2012. "The Minimal Entropy Martingale Measure (MEMM) for a Markov-Modulated Exponential Lévy Model," Asia-Pacific Financial Markets, Springer, vol. 19(1), pages 63-98, March.
    9. Brigo, Damiano & Hanzon, Bernard, 1998. "On some filtering problems arising in mathematical finance," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 53-64, May.
    10. Michael Mania & Marina Santacroce, 2010. "Exponential utility maximization under partial information," Finance and Stochastics, Springer, vol. 14(3), pages 419-448, September.
    11. Ceci, Claudia & Cretarola, Alessandra & Russo, Francesco, 2014. "BSDEs under partial information and financial applications," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2628-2653.
    12. M. Mania & R. Tevzadze & T. Toronjadze, 2007. "$L^2$-approximating pricing under restricted information," Papers 0708.4095, arXiv.org.
    13. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2014. "Hedging of unit-linked life insurance contracts with unobservable mortality hazard rate via local risk-minimization," Papers 1406.6902, arXiv.org.
    14. Michael Mania & Marina Santacroce, 2008. "Exponential Utility Maximization under Partial Information," ICER Working Papers - Applied Mathematics Series 24-2008, ICER - International Centre for Economic Research.

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