Stability of Skorokhod problem is undecidable

A stability result on optimal Skorokhod embedding

Motivated by the model- independent pricing of derivatives calibrated to the real market, we consider an optimization problem similar to the optimal Skorokhod embedding problem, where the embedded Brownian motion needs only to reproduce a finite number of prices of Vanilla options. We derive in this paper the corresponding dualities and the geometric characterization of optimizers. Then we show a stability result, i.e. when more and more Vanilla options are given, the optimization problem converges to an optimal Skorokhod embedding problem, which constitutes the basis of the numerical computat…

平面域的布朗收敛与平面Skorokhod嵌入问题的稳定性

Brownian Convergence of Planar Domains and Stability of the Planar Skorokhod Embedding Problem

本文提出一个数值框架来近似平面Skorokhod嵌入问题中的μ-域，并证明在概率测度序列弱收敛下，相应的μ-域序列在适当意义下收敛到极限测度μ的域，同时给出实现策略、收敛速率估计和数值例子。

Stability for gains from large investors' strategies in M1/J1 topologies

We prove continuity of a controlled SDE solution in Skorokhod's $M_1$ and $J_1$ topologies and also uniformly, in probability, as a non-linear functional of the control strategy. The functional comes from a finance problem to model price impact of a large investor in an illiquid market. We show that $M_1$-continuity is the key to ensure that proceeds and wealth processes from (self-financing) càdlàg trading strategies are determined as the continuous extensions for those from continuous strategies. We demonstrate by examples how continuity properties are useful to solve different stochastic co…

带泊松跳的反射McKean-Vlasov随机微分方程的最优控制问题

Optimal control problem for reflected McKean--Vlasov stochastic differential equations with Poisson jumps

针对一类带泊松跳的一维反射McKean-Vlasov随机微分方程，利用Aldous紧性准则和Skorokhod映射连续性，证明了最优松弛控制的存在性，并在Roxin凸性条件下得到严格最优控制的存在性。

平面Skorokhod嵌入问题的最优设计

Quantitative Brownian Symmetrization: Stability and a Sharp Energy Threshold

本文研究平面Skorokhod嵌入问题的最优设计，通过变分框架证明Gross域在面积最小化中的唯一性，并探讨布朗运动对称化的几何意义。