Continuous-time dynamic risk measures by backward stochastic Volterra integral equations

Jiongmin Yong

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Stochastic processes and financial applications Risk and Portfolio Optimization Fuzzy Systems and Optimization

Abstract

Continuous-time dynamic convex and coherent risk measures are introduced. To obtain existence of such risk measures, backward stochastic Volterra integral equations (BSVIEs, for short) are studied. For such equations, notion of adapted M-solution is introduced, well-posedness is established, duality principles and comparison theorems are presented. Then a class of dynamic convex and coherent risk measures are identified as a component of the adapted M-solutions to certain BSVIEs.

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References

1999Coherent Measures of Risk 1990Adapted solution of a backward stochastic differential equation 1997Backward Stochastic Differential Equations in Finance 2002Convex measures of risk and trading constraints 2007Forward-Backward Stochastic Differential Equations and their Applications 2004Dynamic coherent risk measures 2003Lp solutions of backward stochastic differential equations 2004Nonlinear Expectations, Nonlinear Evaluations and Risk Measures

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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 2020Backward doubly stochastic Volterra integral equations and their applications 2012

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