Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-09T01:36:42.365Z Has data issue: false hasContentIssue false
  • English
  • Français

Hedging contingent claims for a large investor in an incomplete market

Part of: Stochastic analysis

Published online by Cambridge University Press:  01 July 2016

Rainer Buckdahn  and
Ying Hu
Rainer Buckdahn*
Affiliation:
Université de Bretagne Occidentale
Ying Hu*
Affiliation:
Université Blaise Pascal
*
∗ Postal address: Département de Mathématiques, Université de Bretagne Occidentale, 29285 Brest Cédex, France.
∗∗ Postal address: Laboratoire de Mathématiques Appliquées, Université Blaise Pascal - Clermont-Ferrand II, 63177 Aubière Cédex, France.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we study the problem of pricing contingent claims for a large investor (i.e. the coefficients of the price equation can also depend on the wealth process of the hedger) in an incomplete market where the portfolios are constrained. We formulate this problem so as to find the minimal solution of forward-backward stochastic differential equations (FBSDEs) with constraints. We use the penalization method to construct a sequence of FBSDEs without constraints, and we show that the solutions of these equations converge to the minimal solution we are interested in.

Keywords

Forward-backward stochastic differential equationscontingent claimshedging strategylarge investorconstrained portfoliosincomplete markets

MSC classification

Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 1 , March 1998 , pp. 239 - 255
Copyright
Copyright © Applied Probability Trust 1998 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Antonelli, F. (1993). Backward-forward stochastic differential equations. Ann. Appl. Prob. 3, 773–793.Google Scholar
[2] Buckdahn, R. and Hu, Y. (1997). Pricing of American contingent claims with jump stock price and constrained portfolios. Math. Oper. Res. (To appear.).Google Scholar
[3] Cvitanic, J. and Karatzas, I. (1993). Hedging contingent claims with constrained portfolios. Ann. Appl. Prob. 3, 652–681.CrossRefGoogle Scholar
[4] Cvitanic, J. and Ma, J. (1996). Hedging options for a large investor and forward–backward SDEs. Ann. Appl. Prob. 6, 370–398.Google Scholar
[5] El Karoui, N, Peng, S. and Quenez, M.-C. (1997). Backward stochastic differential equations in finance. Math. Finance 7, 1–71.CrossRefGoogle Scholar
[6] El Karoui, N. and Quenez, M.-C. (1995). Dynamic programming and pricing of contingent claims in an incomplete market. SIAM J. Control Optim. 33, 29–66.Google Scholar
[7] Föllmer, H. and Schweizer, M. (1991). Hedging of contingent claims under incomplete information. In Applied Stochastic Analysis ed. Davis, M. H. A. and Elliot, R. J.. Gordon and Breach, New York. pp. 389–414.Google Scholar
[8] Hu, Y. and Peng, S. (1995). Solution of forward–backward stochastic differential equations. Prob. Theory Rel. Fields 103, 273–283.Google Scholar
[9] Ladyzenskaja, O.A., Solonnikov, V.A. and Ural'ceva, N.N. (1968). Linear and Quasilinear Equations of Parabolic Type. American Mathematical Society, Providence, RI.Google Scholar
[10] Ma, J., Protter, P. and Yong, J. (1994). Solving forward–backward stochastic differential equations explicitly: a four step scheme. Prob. Theory Rel. Fields 98, 339–359.CrossRefGoogle Scholar
[11] Pardoux, E. and Peng, S. (1990). Adapted solution of a backward stochastic differential equation. Syst. Control Lett. 14, 55–61.Google Scholar