Second-Order Backward Stochastic Differential Equations and Fully Nonlinear Parabolic PDEs
نویسنده
چکیده
In the probability literature, backward stochastic differential equations (BSDE) received considerable attention after their introduction by E. Pardoux and S. Peng [5, 6] in 1990. During the past decade, interesting connections to partial differential equations (PDE) were obtained and the theory found wide applications in mathematical finance. The key property of the BSDE’s is the random terminal data that the solutions are required to satisfy. Due to the usual adaptedness conditions the stochastic processes are required to satisfy, this condition satisfied in the future introduces additional difficulties in the stochastic setting. However, these difficulties were overcome and an impressive theory is now available. See for instance the survey of ElKaroui, Peng and Quenez [4] and the references therein for this theory and its applications. A backward stochastic differential equation (BSDE in short) is this. We are first given a diffusion process
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