Article2007

NON-LIPSCHITZ BACKWARD STOCHASTIC VOLTERRA TYPE EQUATIONS WITH JUMPS

45 citations0/0 files storedStochastics and Dynamics

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Fuzzy Systems and Optimization

Abstract

In this paper, we prove the existence and uniqueness of solution for the backward stochastic Volterra integral equation with non-Lipschitz coefficients and driven by Brownian motion and jump process. Moreover, when the equation is driven only by Brownian motion, we also study the continuity of the solution with respect to the time.

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References

1990Adapted solution of a backward stochastic differential equation 1991Continuous Martingales and Brownian Motion 1997Backward stochastic differential equations and integral-partial differential equations 1994Necessary Conditions for Optimal Control of Stochastic Systems with Random Jumps 1997Backward stochastic differential equations with continuous coefficient 1995Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients 1997On solutions of backward stochastic differential equations with jumps and applications 1985Volterra Equations Driven by Semimartingales

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2017Optimal Control Problems of Forward-Backward Stochastic Volterra Integral Equations with Closed Control Regions 2009On Solutions of Backward Stochastic Volterra Integral Equations with Jumps in Hilbert Spaces 2014Comparison theorems for some backward stochastic Volterra integral equations 2015Optimal control problems of forward-backward stochastic Volterra integral equations 2019Recursive Utility Processes, Dynamic Risk Measures and Quadratic Backward Stochastic Volterra Integral Equations

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