Smoothing problem in anticipating scenario

Stochastic anticipating boundary value problems

This article is devoted to the stochastic anticipating equations with the extended stochastic integral with respect to the Gaussian processes of a special type. In the particular cases the solutions of such an equations are the well-known Wiener functionals after the second quantization. As an application the stochastic Kolmogorov equation for the conditional distributions of the diffusion process is obtained. Also we will consider the conditional variant of the Feynman--Kac formula. The two last sections of the article are devoted to the smoothing problem in the case when noise is represented…

使用 Skorokhod 与 Russo-Vallois 积分在内幕信息下的最优投资

Optimal investment with insider information using Skorokhod & Russo-Vallois integration

本文研究了内幕知情者在不同预期技术下对数效用的最大化问题，比较了 Russo-Vallois 前向积分与 Skorokhod 积分，发现 Skorokhod 内幕知情人表现更优，但在特定负波动下普通交易者可能反超，揭示了预期随机微积分与非线性效用间复杂的非直观相互作用。

一种具备强收敛性质的指数平均过程

An Exponential Averaging Process with Strong Convergence Properties

针对传统指数移动平均（EMA）因最新观测权重恒定而缺乏强随机收敛性的问题，提出权重以次谐波速率衰减的$p$-EMA方法，给出温和假设下的收敛保证，并探讨其在SGD自适应步长控制中的应用意义。