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Degenerate backward SPDEs in domains: non-local boundary conditions and applications to finance

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  • Nikolai Dokuchaev

Abstract

Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the equation can be degenerate. Some generalized solutions based on the representation theorem are suggested. In addition to problems with a standard Cauchy condition at the terminal time, problems with special non-local boundary conditions are considered. These non-local conditions connect the terminal value of the solution with a functional over the entire past solution. Uniqueness, solvability and regularity results are obtained. Some applications to portfolio selection problem are considered.

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File URL: http://arxiv.org/pdf/1211.5858
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1211.5858.

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Date of creation: Nov 2012
Date of revision: May 2014
Handle: RePEc:arx:papers:1211.5858

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Web page: http://arxiv.org/

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