Maximum principle for stochastic recursive optimal control problem under model uncertainty

A Global Maximum Principle for Controlled Conditional Mean-field FBSDEs with Regime Switching

This paper is devoted to a global stochastic maximum principle for conditional mean-field forward-backward stochastic differential equations (FBSDEs, for short) with regime switching. The control domain is unnecessarily convex and the driver of backward stochastic differential equations (BSDEs, for short) could depend on $Z$. Different from the case of non-recursive utility, the first-order and second-order adjoint equations are both high-dimensional linear BSDEs. Based on the adjoint equations, we reveal the relations among the terms of the first- and second-order Taylor's expansions. A gener…

A Modified Method of Successive Approximations for Stochastic Recursive Optimal Control Problems

Based on the stochastic maximum principle for the partially coupled forward-backward stochastic control system (FBSCS for short), a modified method of successive approximations (MSA for short) is established for stochastic recursive optimal control problems. The second-order adjoint processes are introduced in the augmented Hamiltonian minimization step since the control domain is not necessarily convex. Thanks to the theory of bounded mean oscillation martingales (BMO martingales for short), we give a delicate proof of the error estimate and then prove the convergence of the modified MSA algo…

带有限随机权重的加权递归图中高阶顶点的位置

The location of high-degree vertices in weighted recursive graphs with bounded random weights

该研究探讨了加权递归图中高阶顶点位置的渐近行为，证明了最大度数顶点标签大小的临界指数，并扩展了相关模型的渐近理论。

Stochastic Recursive Optimal Control Problem with Time Delay and Applications

This paper is concerned with a stochastic recursive optimal control problem with time delay, where the controlled system is described by a stochastic differential delayed equation (SDDE) and the cost functional is formulated as the solution to a backward SDDE (BSDDE). When there are only the pointwise and distributed time delays in the state variable, a generalized Hamilton-Jacobi-Bellman (HJB) equation for the value function in finite dimensional space is obtained, applying dynamic programming principle. This generalized HJB equation admits a smooth solution when the coefficients satisfy a pa…

Maximization of recursive utilities under convex portfolio constraints

We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption-investment strategy by studying the associated quadratic backward stochastic differential equation (BSDE in short). We characterize the optimal control by using the duality method and deriving a dynamic maximum principle.

带有莱维噪声的时变前向后向随机控制问题的随机极大原理

Stochastic maximum principle for time-changed forward-backward stochastic control problem with Lévy noise

本文基于时变前向后向随机微分方程建立了随机极大原理，用于最优控制问题，通过对偶变换和凸变分方法推导出最优条件，应用于随机递归效用下的现金管理问题。

基于虚拟粒子的交互粒子系统递归最大似然估计

Recursive Maximum Likelihood Estimation for Interacting Particle Systems using Virtual Particles

本文研究了基于单个粒子连续观测的交互粒子系统递归最大似然估计，通过虚拟交互粒子系统和虚拟切线交互粒子系统，提出在连续时间内利用随机梯度估计的方法，证明在粒子数趋于无穷时，算法收敛于均场系统的平稳对数似然。

Adaptive Robust Control Under Model Uncertainty

In this paper we propose a new methodology for solving an uncertain stochastic Markovian control problem in discrete time. We call the proposed methodology the adaptive robust control. We demonstrate that the uncertain control problem under consideration can be solved in terms of associated adaptive robust Bellman equation. The success of our approach is to the great extend owed to the recursive methodology for construction of relevant confidence regions. We illustrate our methodology by considering an optimal portfolio allocation problem, and we compare results obtained using the adaptive rob…

A survey of max-type recursive distributional equations

In certain problems in a variety of applied probability settings (from probabilistic analysis of algorithms to statistical physics), the central requirement is to solve a recursive distributional equation of the form X =^d g((ξ_i,X_i),i\geq 1). Here (ξ_i) and g(\cdot) are given and the X_i are independent copies of the unknown distribution X. We survey this area, emphasizing examples where the function g(\cdot) is essentially a ``maximum'' or ``minimum'' function. We draw attention to the theoretical question of endogeny: in the associated recursive tree process X_i, are the X_i measurable fun…

Maximum Likelihood With a Time Varying Parameter

We consider the problem of tracking an unknown time varying parameter that characterizes the probabilistic evolution of a sequence of independent observations. To this aim, we propose a stochastic gradient descent-based recursive scheme in which the log-likelihood of the observations acts as time varying gain function. We prove convergence in mean-square error in a suitable neighbourhood of the unknown time varying parameter and illustrate the details of our findings in the case where data are generated from distributions belonging to the exponential family.