论文标题
有条件的McKean-Vlasov跳跃扩散的最佳停止
Optimal stopping of conditional McKean-Vlasov jump diffusions
论文作者
论文摘要
我们研究有条件的McKean-Vlasov（平均场）随机微分方程的最佳停止问题（简而言之的是McKean-Vlasov跳跃扩散）。我们获得了足够的变异不等式，以使函数成为此类问题的价值函数，并且在停止时间最佳。为了实现这一目标，我们将条件McKean-Vlasov方程的状态方程与相关的随机Fokker-Planck方程组合在一起，以解决状态解决方案的条件定律。这为我们提供了一个马尔可夫系统，可以使用Dynkin公式的版本来处理。我们通过明确求解有条件的McKean-Vlasov跳跃扩散的两个最佳停止问题来说明我们的结果。更具体地说，我们首先找到在具有共同噪音和跳跃的市场中出售的最佳时间，接下来，我们发现停止时间以跳跃扩散为模型的项目，当绩效功能涉及状态的条件平均值时。
We study the problem of optimal stopping of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffusions, for short). We obtain sufficient variational inequalities for a function to be the value function of such a problem and for a stopping time to be optimal. To achieve this, we combine the state equation for the conditional McKean-Vlasov equation with the associated stochastic Fokker-Planck equation for the conditional law of the solution of the state. This gives us a Markovian system which can be handled by using a version of the Dynkin formula. We illustrate our result by solving explicitly two optimal stopping problems for conditional McKean-Vlasov jump diffusions. More specifically, we first find the optimal time to sell in a market with common noise and jumps, and, next, we find the stopping time to quit a project whose state is modelled by a jump diffusion, when the performance functional involves the conditional mean of the state.
