We prove the existence of a viscosity solution of the following path dependent nonlinear Kolmogorov equation: where , ≔ and ≔ The result is obtained by a stochastic approach. More precisely, we prove a new type of nonlinear Feynman–Kac representation formula associated to a backward stochastic differential equation with time-delayed generator, which is of non-Markovian type. Applications to the large investor problem and risk measures via –expectations are also provided.

A stochastic approach to path-dependent nonlinear Kolmogorov equations via BSDEs with time-delayed generators and applications to finance

Francesco Cordoni;Luca Di Persio
;
Lucian Maticiuc;Adrian Zalinescu
2020

Abstract

We prove the existence of a viscosity solution of the following path dependent nonlinear Kolmogorov equation: where , ≔ and ≔ The result is obtained by a stochastic approach. More precisely, we prove a new type of nonlinear Feynman–Kac representation formula associated to a backward stochastic differential equation with time-delayed generator, which is of non-Markovian type. Applications to the large investor problem and risk measures via –expectations are also provided.
Path-dependent partial differential equations , Viscosity solutions, Feynman–Kac formula , Backward stochastic differential equations, Time-delayed generators
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11562/1003682
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