Martingale driven BSDEs, PDEs and other related deterministic problems

Adrien Barrasso; Francesco Russo

doi:10.1016/j.spa.2020.11.007

Martingale driven BSDEs, PDEs and other related deterministic problems

Adrien Barrasso
, Francesco Russo

Université d'Evry Val d'Essonne

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We focus on a class of BSDEs driven by a càdlàg martingale and the corresponding Markovian BSDEs which arise when the randomness of the driver appears through a Markov process. To those BSDEs we associate a deterministic equation which, when the Markov process is a Brownian diffusion, is nothing else but a parabolic semi-linear PDE. We prove existence and uniqueness of a decoupled mild solution of the deterministic problem, and give a probabilistic representation of this solution through the aforementioned BSDEs.

Original language	English
Pages (from-to)	193-228
Number of pages	36
Journal	Stochastic Processes and their Applications
Volume	133
DOIs	https://doi.org/10.1016/j.spa.2020.11.007
Publication status	Published - 1 Mar 2021

Keywords

Backward stochastic differential equation
Càdlàg martingale
Decoupled mild solutions
Markov processes
Martingale problem
Pseudo-PDE

Access to Document

10.1016/j.spa.2020.11.007

Cite this

@article{8002968c4d2e4de59623424fde062599,

title = "Martingale driven BSDEs, PDEs and other related deterministic problems",

abstract = "We focus on a class of BSDEs driven by a c{\`a}dl{\`a}g martingale and the corresponding Markovian BSDEs which arise when the randomness of the driver appears through a Markov process. To those BSDEs we associate a deterministic equation which, when the Markov process is a Brownian diffusion, is nothing else but a parabolic semi-linear PDE. We prove existence and uniqueness of a decoupled mild solution of the deterministic problem, and give a probabilistic representation of this solution through the aforementioned BSDEs.",

keywords = "Backward stochastic differential equation, C{\`a}dl{\`a}g martingale, Decoupled mild solutions, Markov processes, Martingale problem, Pseudo-PDE",

author = "Adrien Barrasso and Francesco Russo",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

year = "2021",

month = mar,

day = "1",

doi = "10.1016/j.spa.2020.11.007",

language = "English",

volume = "133",

pages = "193--228",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Martingale driven BSDEs, PDEs and other related deterministic problems

AU - Barrasso, Adrien

AU - Russo, Francesco

PY - 2021/3/1

Y1 - 2021/3/1

N2 - We focus on a class of BSDEs driven by a càdlàg martingale and the corresponding Markovian BSDEs which arise when the randomness of the driver appears through a Markov process. To those BSDEs we associate a deterministic equation which, when the Markov process is a Brownian diffusion, is nothing else but a parabolic semi-linear PDE. We prove existence and uniqueness of a decoupled mild solution of the deterministic problem, and give a probabilistic representation of this solution through the aforementioned BSDEs.

AB - We focus on a class of BSDEs driven by a càdlàg martingale and the corresponding Markovian BSDEs which arise when the randomness of the driver appears through a Markov process. To those BSDEs we associate a deterministic equation which, when the Markov process is a Brownian diffusion, is nothing else but a parabolic semi-linear PDE. We prove existence and uniqueness of a decoupled mild solution of the deterministic problem, and give a probabilistic representation of this solution through the aforementioned BSDEs.

KW - Backward stochastic differential equation

KW - Càdlàg martingale

KW - Decoupled mild solutions

KW - Markov processes

KW - Martingale problem

KW - Pseudo-PDE

U2 - 10.1016/j.spa.2020.11.007

DO - 10.1016/j.spa.2020.11.007

M3 - Article

AN - SCOPUS:85098463974

SN - 0304-4149

VL - 133

SP - 193

EP - 228

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

ER -

Martingale driven BSDEs, PDEs and other related deterministic problems

Abstract

Keywords

Access to Document

Fingerprint

Cite this