Hilbert space-valued forward-backward stochastic differential equations with Poisson jumps and applications |
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Authors: | Juliang Yin Yongjin Wang |
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Affiliation: | a Department of Statistics, Jinan University, Guangzhou 510630, PR China b School of Mathematics, Nankai University, Tianjin 300071, PR China |
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Abstract: | In this paper, we study a class of Hilbert space-valued forward-backward stochastic differential equations (FBSDEs) with bounded random terminal times; more precisely, the FBSDEs are driven by a cylindrical Brownian motion on a separable Hilbert space and a Poisson random measure. In the case where the coefficients are continuous but not Lipschitz continuous, we prove the existence and uniqueness of adapted solutions to such FBSDEs under assumptions of weak monotonicity and linear growth on the coefficients. Existence is shown by applying a finite-dimensional approximation technique and the weak convergence theory. We also use these results to solve some special types of optimal stochastic control problems. |
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Keywords: | Adapted solution Cylindrical Brownian motion Forward-backward SDEs Poisson point process Optimal stochastic control |
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