Viscosity Solutions of Stochastic Hamilton--Jacobi--Bellman Equations with Jumps
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911700204126208 |
|---|---|
| author | Liang, Dunxiang Meng, Qingxin |
| author_facet | Liang, Dunxiang Meng, Qingxin |
| contents | This paper studies the stochastic optimal control of jump-diffusion processes and the associated fully nonlinear backward stochastic Hamilton--Jacobi--Bellman (BSHJB) equations. We establish the dynamic programming principle (DPP) via backward semigroups to characterize the value function. To handle non-local integro-differential operators and polynomial growth, we introduce a stochastic viscosity solution framework based on semimartingale test functions and global tangency conditions. Existence is proved using the measurable selection theorem and the generalized Itô--Kunita formula. Finally, under a super-parabolicity condition, we establish a weak comparison principle and prove global uniqueness via localized bounding envelopes and backward induction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20593 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Viscosity Solutions of Stochastic Hamilton--Jacobi--Bellman Equations with Jumps Liang, Dunxiang Meng, Qingxin Optimization and Control Probability This paper studies the stochastic optimal control of jump-diffusion processes and the associated fully nonlinear backward stochastic Hamilton--Jacobi--Bellman (BSHJB) equations. We establish the dynamic programming principle (DPP) via backward semigroups to characterize the value function. To handle non-local integro-differential operators and polynomial growth, we introduce a stochastic viscosity solution framework based on semimartingale test functions and global tangency conditions. Existence is proved using the measurable selection theorem and the generalized Itô--Kunita formula. Finally, under a super-parabolicity condition, we establish a weak comparison principle and prove global uniqueness via localized bounding envelopes and backward induction. |
| title | Viscosity Solutions of Stochastic Hamilton--Jacobi--Bellman Equations with Jumps |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2605.20593 |