We study the obstacle problem for a class of nonlinear integro-partial differential equations of second order, possibly degenerate, which includes the equation modeling American options in a jump-diffusion market with large investor. The viscosity solutions setting reveals appropriate, because of a monotonicity property with respect to the integral term. The same property allows to approximate the problem by penalization and to obtain the existence and uniqueness of solutions via a comparison principle. We also give uniform estimates of the solutions of the penalized problems which allow to prove further regularity.
Obstacle problem for nonlinear integro-differential equations arising in option pricing
AMADORI, Anna Lisa
2007-01-01
Abstract
We study the obstacle problem for a class of nonlinear integro-partial differential equations of second order, possibly degenerate, which includes the equation modeling American options in a jump-diffusion market with large investor. The viscosity solutions setting reveals appropriate, because of a monotonicity property with respect to the integral term. The same property allows to approximate the problem by penalization and to obtain the existence and uniqueness of solutions via a comparison principle. We also give uniform estimates of the solutions of the penalized problems which allow to prove further regularity.File in questo prodotto:
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