One‐Dimensional Nonlinear Backward Stochastic Differential Equations: A Unified Theory and Applications
该文研究生成元在一元变量线性或超线性增长、二元变量至多二次增长下的一维非线性倒向随机微分方程，建立存在性、唯一性及比较定理，并概述应用和开放问题，适合金融数学与随机控制研究者参考。
ABSTRACT We present a comprehensive theory on the existence and uniqueness of adapted solutions to a one‐dimensional nonlinear backward stochastic differential equation (1D BSDE for short), and assume that the generator has a unilateral linear or super‐linear growth in the first unknown variable , and has an at most quadratic growth in the second unknown variable . We develop a unified methodology, featured by the test function method and the a priori estimate technique, to establish several existence theorems and comparison theorems, which immediately yield corresponding existence and uniqueness results. We also overview relevant known results and give some practical applications of our theoretical results. Finally, we list some open problems on the well‐posedness of 1D BSDEs.