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
2020-01-01
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.File in questo prodotto:
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