One dimensional reflected BSDEs with two barriers under logarithmic growth and applications
| Autor: | Asri, Brahim El, Oufdil, Khalid, Ourkiya, Nacer |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper we deal with the problem of the existence and the uniqueness of a solution for one dimensional reflected backward stochastic differential equations with two strictly separated barriers when the generator is allowing a logarithmic growth $(|y||\ln|y||+|z|\sqrt{|\ln|z||})$ in the state variables $y$ and $z$. The terminal value $\xi$ and the obstacle processes $(L_t)_{0\leq t\leq T}$ and $(U_t)_{0\leq t\leq T}$ are $L^p$-integrable for a suitable $p > 2$. The main idea is to use the concept of local solution to construct the global one. As applications, we broaden the class of functions for which mixed zero-sum stochastic differential games admit an optimal strategy and the related double obstacle partial differential equation problem has a unique viscosity solution. Comment: 26 pages |
| Databáze: | arXiv |
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