کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8904500 1633705 2017 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
BSDES in games, coupled with the value functions. associated nonlocal Bellman-Isaacs equations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
BSDES in games, coupled with the value functions. associated nonlocal Bellman-Isaacs equations
چکیده انگلیسی
We establish a new type of backward stochastic differential equations (BSDEs) connected with stochastic differential games (SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs (HJB-Isaacs) equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair (W,U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs' condition.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Acta Mathematica Scientia - Volume 37, Issue 5, September 2017, Pages 1497-1518
نویسندگان
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