Reflected solutions of backward stochastic differential equations driven by G-Brownian motion

查看全文 作　　者：Hanwu [1]Li;Shige [1,2]Peng;Abdoulaye Soumana [3,4]Hima

机构地区：[1]School of Mathematics, Shandong University, Jinan 250100, China;[2]Zhongtai Institute of Finance, Shangdong University, Jinan 250100, China;[3]Institut de Recherche Mathdmatiques de Rennes, Universitd de Rennes 1, Rennes Cedex 35042, France;[4]Departement de Mathdmatiques, Universite de Maradi, Maradi BP 465, Niger

出　　处：《Science China Mathematics》索引2018年第61卷第1期,共26页

基　　金：supported by the Tian Yuan Projection of the National Natural Science Foundation of China(Grant Nos.11526205 and 11626247);the German Research Foundation(DFG)via CRC1283;the Lebesgue Center of Mathematics(“Investissements d’aveni”Program)(Grant No.ANR-11-LABX-0020-01) 摘　　要：In this paper, we study the reflected solutions of one-dimensional backward stochastic differential equations driven by G-Brownian motion. The reflection keeps the solution above a given stochastic process. In order to derive the uniqueness of reflected G-BSDEs, we apply a 'martingale condition' instead of the Skorohod condition. Similar to the classical case, we prove the existence by approximation via penalization. We then give some applications including a generalized Feynman-Kac formula of an obstacle problem for fully nonlinear partial differential equation and option pricing of American types under volatility uncertainty. 关键词：G-EXPECTATION reflected backward stochastic differential equations obstacle problems for fully nonlinear PDEs

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Reflected solutions of backward stochastic differential equations driven by G-Brownian motion

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