On Exponential Hedging and Related Quadratic Backward Stochastic Differential Equations

Journal Article · Fri Sep 15 00:00:00 EDT 2006 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-006-0855-4· OSTI ID:21064207

Sekine, Jun ^[1]

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1. Institute of Economic Research, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)

The dual optimization problem for the exponential hedging problem is addressed with a cone constraint. Without boundedness conditions on the terminal payoff and the drift of the Ito-type controlled process, the backward stochastic differential equation, which has a quadratic growth term in the drift, is derived as a necessary and sufficient condition for optimality via a variational method and dynamic programming. Further, solvable situations are given, in which the value and the optimizer are expressed in closed forms with the help of the Clark-Haussmann-Ocone formula.

• OSTI ID: 21064207
• Journal Information: Applied Mathematics and Optimization, Vol. 54, Issue 2; Other Information: DOI: 10.1007/s00245-006-0855-4; Copyright (c) 2006 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONES
DIFFERENTIAL EQUATIONS
DYNAMIC PROGRAMMING
OPTIMIZATION
STOCHASTIC PROCESSES
VARIATIONAL METHODS