Abstract
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.
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Sekine, J. On Exponential Hedging and Related Quadratic Backward Stochastic Differential Equations. Appl Math Optim 54, 131–158 (2006). https://doi.org/10.1007/s00245-006-0855-4
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DOI: https://doi.org/10.1007/s00245-006-0855-4