Infinite horizon doubly reflected generalized BSDEs in a general filtration under stochastic conditions

Mohammed Elhachemy; Badr Elmansouri; Mohamed El Otmani

doi:10.5269/bspm.68171

Mohammed Elhachemy Ibn Zohr University
Badr Elmansouri Laboratory of Analysis, Mathematics and Applications (LAMA), Faculty of Sciences Agadir, Ibn Zohr University https://orcid.org/0000-0003-2603-894X
Mohamed El Otmani Laboratory of Analysis, Mathematics and Applications (LAMA), Faculty of Sciences Agadir, Ibn Zohr University https://orcid.org/0000-0002-9674-6469

Resumo

In this paper, we explore a significant class of double reflected generalized backward stochastic differential equations in a general filtration framework that supports a Brownian motion and an independent integer-valued random measure. Specifically, when the barriers are right-continuous, left-limited, and completely separated, and that the generators satisfy stochastic conditions, we establish both the existence and uniqueness of a solutions when the time horizon is infinite.

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Referências

Bahlali, K., Elouaflin, A., and N’zi, M., Backward stochastic differential equations with stochastic monotone coefficients, J. Appl. Math. Stoch. Anal., 2004, 317–335, (2004).

Bender, C., and Kohlmann, M. , Bsdes with stochastic lipschitz condition, Technical report, CoFE Discussion Paper, (2000).

Chen, Z., Existence and uniqueness for bsde with stopping time, Chinese Sci. Bull. 43, 96–99, (1998).

Chung, K. L., A course in probability theory, Academic Press, 2001.

Dellacherie, C., and Meyer, P., Probabilit´es et Potentiel, Chap. I-IV, Hermann, (1975).

Elhachemy, M., and El Otmani, M., Reflected generalized discontinuous BSDEs with rcll barrier and an obstacle problem of IPDE with nonlinear Neumann boundary conditions, Mod. Stoch. Theory Appl., 10(1) ,77–110, (2023).

El Karoui, N., and Huang, S., A general result of existence and uniqueness of backward stochastic differential equations, Pitman research notes in mathematics series, 27–38, (1997).

El Otmani, M., Generalized BSDE driven by a L´evy process, J. Appl. Math. Stoch. Anal., 2006, 1–26, (2006).

El Otmani, M, and Mrhardy, N., Generalized BSDE with two reflecting barriers, Random Operators and Stochastic Equations, 16 (4), 357-382, (2008).

Hamadene, S., Lepeltier, J.-P. and Wu, Z., Infinite horizon reflected backward stochastic differential equations and applications in mixed control and game problems, Probab. Math. Stat.-Wroclaw Univ., 19, 211–234, (1999).

Hua, W., Jiang, L., and Shi, X., Infinite time interval rbsdes with non-lipschitz coefficients, J. Korean Statist. Soc., 42, 247–256, (2013).

Jacod, J., and Shiryaev, A., Limit theorems for stochastic processes, Springer Science & Business Media, (2013).

Marzougue, M., and El Otmani, M., Double barrier reflected bsdes with stochastic lipschitz coefficient, Mod. Stoch. Theory Appl., 4, 353–379, (2017).

Marzougue, M., El Otmani, M., Reflected bsdes with jumps and two rcll barriers under stochastic lipschitz coefficient, Comm. Statist. Theory Methods., 50, 6049–6066, (2021).

Pardoux, E., Generalized Discontinuous Backward Stochastic Differential Equations, Pitman Research Notes in Mathematics Series, 207–219, (1997).

Pardoux, E., and Peng S., Adapted solution of a backward stochastic differential equation, Systems Control Lett., 14, 55–61, (1990).

Pardoux, E., and R˜ascanu, A., Stochastic differential equations, Backward SDEs, Partial differential equations, volume 69, Springer, (2014).

Pardoux, E., and Zhang, S., Generalized BSDEs and nonlinear Neumann boundary value problems, Probab. Theory Related Fields, 110, 535–558, (1998).

Protter, P. E., Stochastic integration and differential equations, Applications of mathematics 21 0172-4568, Springer, 2004.

Ren, Y., and El Otmani, M., Generalized reflected BSDEs driven by a L´evy process and an obstacle problem for PDIEs with a nonlinear Neumann boundary condition, J. Comput. Appl. Math., 233, 2027–2043, (2010).

Ren, Y., and Xia, N., Generalized reflected BSDE and an obstacle problem for PDEs with a nonlinear Neumann boundary condition, Stoch. Anal. Appl., 24, 1013-33, (2006).

Yosida, K., Functional analysis, Grundlehren der mathematischen Wissenschaften, Springer-Verlag, (1980).