Discrete-Time BSDEs with Random Terminal Horizon |
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Authors: | Yin Lin |
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Institution: | Department of Statistics and Actuarial Science , The University of Hong Kong , Pokfulam Road , Hong Kong |
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Abstract: | This article studies the theory of discrete-time backward stochastic differential equations (also called BSDEs) with a random terminal time, which is not a stopping time. We follow Cohen and Elliott 2
Cohen , S.N. , and
Elliott , R.J. 2010 . A general theory of finite state backward stochastic difference equations . Stochastic Processes and Their Applications 120 ( 4 ): 442 – 466 .Crossref], Web of Science ®] , Google Scholar]] and consider a reference filtration generated by a general discrete-time finite-state process. The martingale representation theorem for essentially bounded martingales under progressively enlarged filtration is established. Then we prove the existence and uniqueness theorem of BSDEs under enlarged filtration using some weak assumptions of the driver. We also present conditions for a comparison theorem. Applications to nonlinear expectations and optimal design of dynamic default risk are explored. |
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Keywords: | BSDE Comparison theorem Defaultable contingent claims Nonlinear expectations Progressively enlarged filtration Random terminal horizon Risk measures |
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