| Autor: |
Hidekazu Yoshioka, Yumi Yoshioka |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| Zdroj: |
Journal of Mathematics in Industry, Vol 13, Iss 1, Pp 1-28 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2190-5983 |
| DOI: |
10.1186/s13362-023-00135-4 |
| Popis: |
Abstract Hamilton–Jacobi–Bellman equation (HJBE) and backward stochastic differential equation (BSDE) are the two faces of stochastic control. We explore their equivalence focusing on a system of self-exciting and affine stochastic differential equations (SDEs) arising in streamflow dynamics. Our SDE is a finite-dimensional Markovian embedding of an infinite-dimensional jump-driven process called the superposition of continuous-state branching processes (a supCBI process). We formulate new ergodic control problems to evaluate the worst-case streamflow discharge in the long run and derive their HJBEs and ergodic BSDEs. The constant ambiguity aversion classically used in assessing model ambiguity must be modified in our case so that the optimality equations become well-posed. With a suitable modification of the ambiguity-aversion coefficient depending on the distributed reversion speed, we demonstrate that the solutions to the optimality equations are equivalent to each other in the sense that they lead to the same result. Finally, we apply the proposed framework to the computation of realistic cases with an existing record of discharge through a numerical Markovian embedding. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
|
|
Nepřihlášeným uživatelům se plný text nezobrazuje |
K zobrazení výsledku je třeba se přihlásit.
|
