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A Stochastic Representation for Nonlocal Parabolic PDEs with Applications

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Document pages: 32 pages

Abstract: We establish a stochastic representation for a class of nonlocal parabolic terminal-boundary value problems, whose terminal and boundary conditions depend on the solution in the interior domain; in particular, the solution is represented as the expectation of functionals of a diffusion process with random jumps from boundaries. We discuss three applications of the representation, the first one on the pricing of dual-purpose funds, the second one on the connection to regenerative processes, and the third one on modeling the entropy on a one-dimensional non-rigid body.

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