**随机控制及相关领域青年学者研讨会**

**1****月12日学术报告，报告地点：山东大学中心校区知新楼B1238 ，邀请人：聂天洋**

**09:30-10:20 ****张鑫**

**Open-Loop and Closed-Loop Solvabilities for Stochastic Linear Quadratic Optimal Control Problems of Markov Regime-Switching System**

**10:20-11:00 ****郑国强**

**G-BSDE with uniformly continuous generators in Z**

**11:00-11:40 ****吕思宇**

**Optimal Switching under a Hybrid Diffusion Model and Applications to Stock Trading**

**14:00-16:30 学术讨论交流**

**报告摘要**

**Open-Loop and Closed-Loop Solvabilities for Stochastic Linear Quadratic Optimal Control Problems of Markov Regime-Switching System**

**张鑫 东南大学**

Abstract: This paper investigates the stochastic linear quadratic (LQ, for short) optimal control problem of Markov regime switching system. The representation of the cost functional for the stochastic LQ optimal control problem of Markov regime switching system is derived using the technique of Itô’s formula. For the stochastic LQ optimal control problem of Markov regime switching system, we establish the equivalence between the open-loop (closed-loop) solvability and the existence of an adapted solution to the corresponding forward-backward stochastic differential equation with constraint (the existence of a regular solution to the Riccati equation). Also, we analyze the interrelationship between the strongly regular solvability of the Riccati equation and the uniform convexity of the cost functional.

张鑫，东南大学数学学院副教授，硕士生导师。南开大学理学博士，澳大利亚Macquarie大学博士后。研究方向为数理金融、精算数学和随机控制。主持国家自然科学基金面上项目2项，在控制论和数理金融领域著名权威期刊SICON、IME等发表SCI论文20余篇。

**G-BSDE with uniformly continuous generators in Z**

**郑国强**** ****东南大学**

We investigate the existence and uniqueness of solutions to a class of non-Lipschitz scalar valued backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs). In fact, when the generators of $G$-BSDEs are Lipschitz continuous in $y$ and uniformly continuous in $z$, we construct the unique solution to such equations by monotone convergence argument. The comparison theorem and related Feynman-Kac formula are stated as well.

郑国强，东南大学数学学院讲师。研究方向为随机分析、非线性期望、倒向随机微分方程。主要研究了G-扩散过程的遍历问题、G-期望下拟连续随机变量和随机过程、G-布朗运动的轨道性质等。在随机分析权威期刊SPA等发表文章多篇。

**Optimal Switching under a Hybrid Diffusion Model and Applications to Stock Trading**

**吕思宇** **东南大学**

Abstract: This talk is concerned with the optimal switching problem under a hybrid diffusion (or, regime switching) model in an infinite horizon. The state of the system consists of a number of diffusions coupled by a finite-state continuous-time Markov chain. Based on the dynamic programming principle, the value function of our optimal switching problem is proved to be the unique viscosity solution to the associated system of variational inequalities. The optimal switching strategy, indicating when and where it is optimal to switch, is given in terms of the switching and continuation regions. In many applications, the underlying Markov chain has a large state space and exhibits two-time-scale structure. In this case, a singular perturbation approach is employed to reduce the computational complexity involved. It is shown that as the time-scale parameter goes to zero, the value function of the original problem converges to that of a limit problem. The limit problem is much easier to solve, and its optimal switching solution leads to an approximate solution to the original problem. Finally, as an application of our theoretical results, an example concerning the stock trading problem in a regime switching market is provided. It is emphasized that, this paper is the first time to introduce the optimal switching as a general framework to study the stock trading problem, in view of their inherent connection. Both optimal trading rule and convergence result are numerically demonstrated in this example. This is a joint work with Profs Zhen Wu and Qing Zhang.

吕思宇，东南大学数学学院讲师，主持国家青年基金一项。研究方向为马尔科夫链、随机控制、金融数学等。主要研究了状态转换下的正倒向随机控制问题及其金融应用。在控制论领域权威期刊Automatica等发表文章多篇。