On Solutions of Backward Stochastic Differential Equations with Jumps and Stochastic Control

Situ Rong
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Situ Rong: Zhongshan University, Department of Mathematics

Chapter Chapter 19 in Markov Processes and Controlled Markov Chains, 2002, pp 331-340 from Springer

Abstract: Abstract We relax conditions on coefficients given in [7] for the existence of solu-tions to backward stochastic differential equations (BSDE) with jumps. Counter examples are given to show that such conditions can not be weakened further in some sense. The existence of a solution for some continuous BSDE with coefficients b(t, y, q) having a quadratic growth in q, having a greater than linear growth in y, and are unbounded in y belonging to a finite interval, is also obtained. Then we obtain an existence and uniqueness result for the Sobolev solution to some integro-differential equation (IDE) under weaker conditions. Some Markov properties for solutions to BSDEs associated with some forward SDEs are also discussed and a Feynman-Kac formula is also obtained. Finally, we obtain probably the first results on the existence of non-Lipschitzian optimal controls for some special stochastic control problems with respect to such BSDE systems with jumps, where some optimal control problem is also explained in the financial market.

Keywords: MARKOV Process; Optimal Control Problem; Stochastic Differential Equation; Markov Property; Stochastic Control (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-0265-0_19

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DOI: 10.1007/978-1-4613-0265-0_19

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