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:
| File | Dimensione | Formato | |
|---|---|---|---|
|
1602.05793.pdf
accesso aperto
Descrizione: arXiv version
Tipologia:
Documento in Pre-print
Licenza:
Dominio pubblico
Dimensione
390.57 kB
Formato
Adobe PDF
|
390.57 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
