Optimal stopping under g-Expectation with -integrable reward process
| Autor: | Mun-Chol Kim, Hun O, Ho-Jin Hwang |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Journal of Applied Probability. 60:241-252 |
| ISSN: | 1475-6072 0021-9002 |
| Popis: | In this paper we study a class of optimal stopping problems under g-expectation, that is, the cost function is described by the solution of backward stochastic differential equations (BSDEs). Primarily, we assume that the reward process is $L\exp\bigl(\mu\sqrt{2\log\!(1+L)}\bigr)$ -integrable with $\mu>\mu_0$ for some critical value $\mu_0$ . This integrability is weaker than $L^p$ -integrability for any $p>1$ , so it covers a comparatively wide class of optimal stopping problems. To reach our goal, we introduce a class of reflected backward stochastic differential equations (RBSDEs) with $L\exp\bigl(\mu\sqrt{2\log\!(1+L)}\bigr)$ -integrable parameters. We prove the existence, uniqueness, and comparison theorem for these RBSDEs under Lipschitz-type assumptions on the coefficients. This allows us to characterize the value function of our optimal stopping problem as the unique solution of such RBSDEs. |
| Databáze: | OpenAIRE |
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