A general stochastic maximum principle for mixed relaxed-singular control problems

最优平稳奇异控制与平均场博弈均衡的存在性

Existence of Optimal Stationary Singular Controls and Mean Field Game Equilibria

本文研究多维平稳松弛奇异控制及其平均场博弈，通过鞅问题与平稳前向方程的等价性将控制问题转化为测度空间线性规划，并利用不动点定理证明平均场博弈均衡存在。

Linearisation Techniques and the Dual Algorithm for a Class of Mixed Singular/Continuous Control Problems in Reinsurance. Part I: Theoretical Aspects

This paper focuses on linearisation techniques for a class of mixed singular/continuous control problems and ensuing algorithms. The motivation comes from (re)insurance problems with reserve-dependent premiums with Cram{é}r-Lundberg claims, by allowing singular dividend payments and capital injections. Using variational techniques and embedding the trajectories in an appropriate family of occupation measures, we provide the linearisation of such problems in which the continuous control is given by reinsurance policies and the singular one by dividends and capital injections. The linearisation …

On singular control problems, the time-stretching method, and the weak-M1 topology

We consider a general class of singular control problems with state constraints. Budhiraja and Ross (2006) established the existence of optimal controls for a relaxed version of this class of problems by using the so-called `time-stretching' method and the J1-topology. We show that the weak-M1 topology is better suited for establishing existence, since it allows to bypass the time-transformations, without any additional effort. Furthermore, we reveal how the time-scaling feature in the definition of the weak-M1 distance embeds the time-stretching method's scheme. This case study suggests that …

Mixed Boundary Value Problems of Semilinear Elliptic PDEs and BSDEs with Singular Coefficients

In this paper, we prove that there exists a unique weak solution to the mixed boundary value problem for a general class of semilinear second order elliptic partial differential equations with singular coefficients. Our approach is probabilistic. The theory of Dirichlet forms and backward stochastic differential equations with singular coefficients and infinite horizon plays a crucial role.

双混合分数布朗运动中通过Fredholm方程解的漂移参数估计

Drift parameter estimation in the double mixed fractional Brownian model via solutions of Fredholm equations with singular kernels

本文提出了一种通过将算子方程转化为Fredholm积分方程来近似求解的方法，用于双混合分数布朗运动模型中的漂移参数估计。

A mixed singular/switching control problem for a dividend policy with reversible technology investment

We consider a mixed stochastic control problem that arises in Mathematical Finance literature with the study of interactions between dividend policy and investment. This problem combines features of both optimal switching and singular control. We prove that our mixed problem can be decoupled in two pure optimal stopping and singular control problems. Furthermore, we describe the form of the optimal strategy by means of viscosity solution techniques and smooth-fit properties on the corresponding system of variational inequalities. Our results are of a quasi-explicit nature. From a financial vie…