A new type of extended backward stochastic Volterra integral equation is shown to provide a probabilistic representation for a non-local quasilinear parabolic PDE, generalizing the Pardoux-Peng Feynman-Kac formula.
Dynamic risk measure for BSVIE with jumps and semimartingale issues
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abstract
Risk measure is a fundamental concept in finance and in the insurance industry, it is used to adjust life insurance rates. In this current paper, we will study dynamic risk measures by means of backward stochastic Volterra integral equations (BSVIEs) with jumps. We prove a comparison theorem for such a type of equations. Since the solution of a BSVIEs is not a semimartingale in general, we will discuss some particular semimartingale issues.
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Extended Backward Stochastic Volterra Integral Equations, Quasilinear Parabolic Equations, and Feynman-Kac Formula
A new type of extended backward stochastic Volterra integral equation is shown to provide a probabilistic representation for a non-local quasilinear parabolic PDE, generalizing the Pardoux-Peng Feynman-Kac formula.