标题：Properties of gΓ-solution and risk measure induced by gΓ-solution
作者：Sui, Yuanyuan ;Wu, Helin
作者机构：[Sui, Yuanyuan ;Wu, Helin ] School of Mathematics, Shandong University, Jinan, 250100, China
会议名称：32nd Chinese Control Conference, CCC 2013
会议日期：July 26, 2013 - July 28, 2013
来源：Chinese Control Conference, CCC
摘要：In this paper, some main properties of the gΓ-solution of a constrained backward stochastic differential equation (CBSDE) are presented and a kind of risk measure induced by the gΓ-solution is proposed. These fine properties make the risk measure become a satisfactory tool for solving the hedging problem in an incomplete market. More importantly, the infconvolution of the convex risk measures can be adopted to deal with some optimization problems involving a transformation of the initial risk measures. Some results about the dynamic version of the inf-convolution of the gΓ-solutions will also be given, just like the usual case without constraints, the inf-convolution of two gΓ-solutions of CBSDEs with different coefficients is equivalent to the gΓ- solution of CBSDE with the inf-convolution of the two coefficients. In this case, it is possible to characterize the optimal risk transfer. © 2013 TCCT, CAA.