论文标题
I型I型向后随机Volterra积分方程的统一方法
A unified approach to well-posedness of type-I backward stochastic Volterra integral equations
论文作者
论文摘要
我们研究了一类新的多维I型向后随机Volterra积分方程。为了实现这一目标，我们引入了标准向后SDE的无限维度系统，并建立了良好的态度，我们表明它等同于I型向后的随机Volterra积分方程。我们还根据汉密尔顿 - 雅各比 - 贝尔曼类型的非线性半线性部分微分方程来建立表示公式。作为应用程序，我们从游戏理论的角度考虑了时间不一致的随机控制。我们从概率和分析的角度表明了两种当前方法对此问题的等效性。
We study a novel general class of multidimensional type-I backward stochastic Volterra integral equations. Toward this goal, we introduce an infinite dimensional system of standard backward SDEs and establish its well-posedness, and we show that it is equivalent to that of a type-I backward stochastic Volterra integral equation. We also establish a representation formula in terms of non-linear semilinear partial differential equation of Hamilton-Jacobi-Bellman type. As an application, we consider the study of time-inconsistent stochastic control from a game-theoretic point of view. We show the equivalence of two current approaches to this problem from both a probabilistic and an analytic point of view.
