Obstacle problem for nonlinear integro-differential equations arising in option pricing |
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Authors: | Anna Lisa Amadori |
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Institution: | (1) Università di Napoli “Parthenope”, Dipartimento di Scienze Applicate, via A. De Gasperi, 5, 80133 Napoli, Italy |
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Abstract: | 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.
Keywords: Integro-differential equations, Obstacle problem, Viscosity solutions, American options
Mathematics Subject Classification (2000): 45K05, 35K85, 49L25, 91B24 |
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