Risk-sensitive Dynkin games with heterogeneous Poisson random intervention times

零和Dynkin游戏在共同和独立泊松约束下

Zero-sum Dynkin games under common and independent Poisson constraints

本文研究了在共同和独立泊松约束下零和Dynkin游戏的解等价性，通过马尔可夫框架和BSDE技术，建立了价值函数和最优停止集的条件，展示了无限时间跨度游戏的适用性。

Dynkin games with Poisson random intervention times

This paper introduces a new class of Dynkin games, where the two players are allowed to make their stopping decisions at a sequence of exogenous Poisson arrival times. The value function and the associated optimal stopping strategy are characterized by the solution of a backward stochastic differential equation. The paper further applies the model to study the optimal conversion and calling strategies of convertible bonds, and their asymptotics when the Poisson intensity goes to infinity.

Optimal Switching at Poisson Random Intervention Times

This paper introduces a new class of optimal switching problems, where the player is allowed to switch at a sequence of exogenous Poisson arrival times, and the underlying switching system is governed by an infinite horizon backward stochastic differential equation system. The value function and the optimal switching strategy are characterized by the solution of the underlying switching system. In a Markovian setting, the paper gives a complete description of the structure of switching regions by means of the comparison principle.

Ergodic control of diffusions with random intervention times

We study an ergodic singular control problem with constraint of a regular one-dimensional linear diffusion. The constraint allows the agent to control the diffusion only at jump times of independent Poisson process. Under relatively weak assumptions, we characterize the optimal solution as impulse type control policy, where it is optimal to exert the exact amount of control needed to push the process to a unique threshold. Moreover, we discuss the connection of the present problem to ergodic singular control problems, and finally, illustrate the results with different well-known cost and diffu…

Optimal Maintenance Policy for a Compound Poisson Shock Model

Engineered and infrastructure systems deteriorate (e.g., loss capacity) as a result of adverse environmental or external conditions. Modeling deterioration is essential to define optimum design strategies and inspection and maintenance (intervention) programs. In particular, the main purpose of maintenance is to increase the system availability by extending the life of the system. Most strategies for maintenance optimization focus on defining long term strategies based on the system's condition at the decision time (e.g., $t=0$). However, due to the large uncertainty in the system's performanc…

带约束奇异控制的平稳遍历平均场博弈

Stationary Ergodic Mean-field Games of Constrained Singular Controls

该研究针对带约束奇异控制的平稳遍历平均场博弈，推导了泊松阈值奇异控制的平稳分布，证明了平稳平均场均衡的存在唯一性，为相关投资案例研究提供了易处理框架。