具有斜次梯度的随机变分不等式

McKean-Vlasov multivalued stochastic differential equations with oblique subgradients and related stochastic control problems

In this article, we prove the existence of weak solutions as well as the existence and uniqueness of strong solutions for McKean-Vlasov multivalued stochastic differential equations with oblique subgradients (MVMSDEswOS, for short) by means of the equations of Euler type and Skorohod's representation theorem. For this type of equation, compared with the method in [19,13], since we can't use the maximal monotony property of its constituent subdifferential operator, some different specific techniques are applied to solve our problems. Afterwards, we give an example for MVMSDEswOS with time-depen…

具有斜次梯度的多值倒向随机微分方程

Multivalued backward stochastic differential equations with oblique subgradients

研究了一类带斜反射的倒向随机变分不等式（简称$BSVI\left(H(t,y),φ,F\right)$）的微分形式\[ \left\{\begin{array} [c]{l}% -dY_{t}+H\left(t,Y_{t}\right) \partialφ\left(Y_{t}\right) \left(dt\right) \ni F\left(t,Y_{t},Z_{t}\right) dt-Z_{t}dB_{t},\quad t\in\left[ 0,T\right] ,\smallskip\\ Y_{T}=η, \end{array} \right. \]的解的存在唯一性，其中$H$是有界对称光滑矩阵，$φ$是真凸下连续函数，$\partialφ$是它的次微分算子.产品$H\partialφ$的存在不允许使用标准的技术，因为它既不保存Lipschitz属性的矩阵，也不单调性能的次微分算子。我们证明了，如果我们只考虑$H$对时间的依赖性，则方程存在唯一的强解，并且，如果也考虑对系统状态的依赖性，则上述$BSVI\left(H(t,y),φ,F\right)$存在Meyer-Zheng拓扑意义下的弱解.然而，为了这个目的，我们必须放弃对生成函数的$Z$的依赖，我们在马尔可夫框架中解决我们的问题。

由鞅噪声驱动且具有斜次梯度的倒向随机动力学的Càdlàg解

Càdlàg Solutions to Backward Stochastic Dynamics featuring Oblique Subgradients and driven by Martingale Noise

本研究针对倒向随机变分动力学，在放宽有界性条件至仿射/二次下界假设下，证明了强càdlàg解的存在唯一性，并引入时间依赖正定矩阵控制的斜反射，克服了现有研究的局限。

具有斜反射和最优开关的多维BSDE

Multi-dimensional BSDE with Oblique Reflection and Optimal Switching

本文研究了一类带斜反射的多维倒向随机微分方程，它是在一个特殊的无界凸区域的边界上沿斜方向反射的随机微分方程，是在研究最优切换问题时自然产生的.通过惩罚方法、单调收敛性和先验估计得到了适应解的存在性。的唯一性得到的验证方法（任何适应的解决方案的第一个组成部分被证明是一个切换问题的BSDES的向量值）。作为应用，我们将上述结果应用于求解泛函型随机微分方程的最优切换问题，并给出了一类变分不等式黏性解的概率解释.

Systems of quasi-variational inequalities related to the switching problem

We prove the existence of weak solution for a system of quasi-variational inequalities related to a switching problem with dynamic driven by operator associated with a semi-Dirichlet form and with measure data. We give a stochastic representation of solutions in terms of solutions of a system of reflected BSDEs with oblique reflection. As a by-product, we prove the existence of an optimal strategy in the switching problem and show regularity of the payoff function.

Stochastic optimal switching and systems of variational inequalities with interconnected obstacles

This paper studies a system of $m$ variational inequalities with interconnected obstacles in infinite horizon associated to optimal multi-modes switching problems. Our main result is the existence and uniqueness of a continuous solution in viscosity sense, for that system. The proof of the main result strongly relies on the connection between the systems of variational inequalities and reflected backward stochastic differential equations (RBSDEs) with oblique reflection, which will be characterized through a Feynman-Kac's formula. The main feature of our system of infinite horizon RBSDEs is th…