Coupled forward-backward stochastic differential equations with jumps in random environments

Fuente: arXiv
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Main Authors: Hernández-Hernández, Daniel, Ricalde-Guerrero, Joshué Helí
Format: Preprint
Published: 2023
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author Hernández-Hernández, Daniel
Ricalde-Guerrero, Joshué Helí
author_facet Hernández-Hernández, Daniel
Ricalde-Guerrero, Joshué Helí
contents In this paper we obtain results for the existence and uniqueness of solutions to coupled Forward-Backward Stochastic Differential Equations (FBSDEs) with jumps defined on a random environment. This environment corresponds to a measured-valued process, similar to the one found in Conditional McKean-Vlasov Differential Equations and Mean-Field Games with Common Noise. The jump term in the FBSDE is dependent on the environment through a stochastic intensity process. We provide examples which relate our model with FBSDEs driven by Cox and Hawkes processes, as well as regime-switching Conditional McKean-Vlasov differential equations.
format Preprint
id arxiv_https___arxiv_org_abs_2307_14318
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Coupled forward-backward stochastic differential equations with jumps in random environments
Hernández-Hernández, Daniel
Ricalde-Guerrero, Joshué Helí
Probability
60K37, 60J76, 60G55
In this paper we obtain results for the existence and uniqueness of solutions to coupled Forward-Backward Stochastic Differential Equations (FBSDEs) with jumps defined on a random environment. This environment corresponds to a measured-valued process, similar to the one found in Conditional McKean-Vlasov Differential Equations and Mean-Field Games with Common Noise. The jump term in the FBSDE is dependent on the environment through a stochastic intensity process. We provide examples which relate our model with FBSDEs driven by Cox and Hawkes processes, as well as regime-switching Conditional McKean-Vlasov differential equations.
title Coupled forward-backward stochastic differential equations with jumps in random environments
topic Probability
60K37, 60J76, 60G55
url https://arxiv.org/abs/2307.14318