Coupled forward-backward stochastic differential equations with jumps in random environments
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929213684056064 |
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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 |