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Entropic Conditions and Hedging

Published online by Cambridge University Press:  19 June 2007

Samuel Njoh
Samuel Njoh*
Affiliation:
Université de Marne-La-Vallée, Cité Descartes, 5, Bld Descartes, Champs-Sur-Marne, 77454 Marne-La-Vallée Cedex 2, France; [email protected]
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Abstract

In many markets, especially in energy markets, electricity markets for instance, the detention of the physical asset is quite difficult. This is also the case for crude oil as treated by Davis (2000). So one can identify a good proxy which is an asset (financial or physical) (one)whose the spot price is significantly correlated with the spot price of the underlying (e.g. electicity or crude oil). Generally, the market could become incomplete. We explicit exact hedging strategies for exponential utilities when the risk premium is bounded. Our result is based upon backward stochastic differential equation (BSDE) and a good choice of admissible strategies which allows us to solve our hedging problem.

Keywords

Stochastic optimizationmartingale representation theorem.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 197 - 216
Copyright
© EDP Sciences, SMAI, 2007

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References

D. Becherer, Rational Hedging and Valuation with Utility-Based Preference. PhD Thesis, Berlin University (2001).
D. Becherer, Rational Hedging and Valuation of Integrated Risks under Constant Absolute Risk Aversion, Insurance: Math. Econ. 33 (2003) 1–28.
J. Cvitanic, W. Schachermayer and H. Wang, Utility Maximization in Incomplete Market with Random Endowment, in Proceedings of Symposia in Applied Mathematics (1999).
M. Davis, Optimal Hedging with Basis Risk, preprint (2000).
M. Davis, Option Valuation and Hedging with Basis Risk, in System Theory: Modeling, Analysis and Control, T.E. Djaferis and I.C. Schick Eds., Kluwer, Amsterdam (1999).
F. Delbaen and W. Schachermayer, Arbitrage and Free Lunch with Bounded Risk for Unbounded Continuous Processes, Mathematical Finance 4 (1994) 343–348.
Delbaen, F., Grandits, P., Rheinlander, T., Samperi, D., Schweizer, M. and Stricker, C., Exponential Hedging and Entropic Penalties. Mathematical Finance 12 (2002) 99–123. CrossRef
N. El Karoui and R. Rouge, Pricing via Utility Maximization and Entropy, Mathematical Finance 10 (2000) 259–276.
W.H. Fleming and R.W. Rishel, Deterministic and Stochastic Optimal Control. Springer Verlag, New York (1975).
V. Henderson, Valuation of Claims of Non Traded Assets using Utility Maximization, Mathematical Finance 12 (2002) 351–373.
Y.M. Kabanov and C. Stricker, On the Optimal Portfolio for the Exponential Utility Maximization: Remarks to the Six-Author Paper, Mathematical Finance 12 (2002) 125–134.
I. Karatzas and S.E. Shreve, Methods of Mathematical Finance. Springer Verlag, New York (1998).
I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus. Springer Verlag (1991).
M. Kobylanski, Backward Stochastic Differential Equations and Partial Differential Equations with Quadratic Growth, The Annals of Probability 2 (2000) 558–602.
D. Revuz and M. Yor, Continuous Martingales and Brownian Motion. Springer Verlag (1991).
W. Schachermayer, Optimal Investment in an Incomplete Market, in H. Geman et al. Eds. Mathematical Finance Bachelier Congress (2000), Berlin Heidelberg New York, Springer (2002).
M. Yor. Sous-Espaces Denses dans L 1 ou H 1, in Séminaire de Probabilités XII, Springer Verlag (1978) 265–309.