精算论坛讲座第109期--倪元华张鑫夏建明  

(10月30日)

报告一：

题目：Time-InconsistentMean-Field Stochastic Linear-Quadratic Optimal Control

报告人：

倪元华（副教授，南开大学计算机与控制工程学院）

    主要研究方向是随机控制理论及其应用，主要文章发表在SIAM J.Control and Optimization, Automatica, IEEE Trans. Automatic Control上，并获得自动化学会2016年度关肇直奖。

时间：10月30日9:00—10:00

摘要：Thispaper is concerned with the open-loop time-consistent solution oftime-inconsistent mean-field stochastic linear-quadratic optimal control.Different from standard stochastic linear-quadratic problems, both the systemmatrices and the weighting matrices are depending on the initial times, and theconditional expectations of the control and state enter quadratically into thecost functional. Such features will ruin Bellman's principle of optimality andresult in the time-inconsistency of optimal control. Based on the dynamicalnature of the systems involved, a kind of open-loop time-consistent equilibriumcontrol is investigated in this paper. It is shown that the existence ofopen-loop equilibrium control for a fixed initial pair is equivalent to thesolvability of a set of forward-backward stochastic difference equations withstationary condition and convexity condition. By decoupling theforward-backward stochastic difference equations, necessary and sufficientconditions in terms of linear difference equations and generalized differenceRiccati equations are given for the existence of open-loop equilibrium controlwith a fixed initial pair. Moreover, the existence of open-loop time-consistentequilibrium controls for all the initial pairs is shown to be equivalent to thesolvability of a set of coupled constrained generalized difference Riccatiequations and two sets of constrained linear difference equations.

报告二：

题目：Bondand option pricing for interest rate model with clustering effects

报告人：张鑫，东南大学数学学院副教授。2009年7月毕业于南开大学数学科学学院并留校任教，2011年赴澳大利亚Macquarie大学做博士后研究，2012年在南开大学晋升副教授，2014年3月访问英国利物浦大学, 2014年7月调入东南大学数学学院。自2006年攻读博士学位以来，主要从事随机过程在金融保险中的应用方面的研究,共发表论文20余篇, 完成国家自然科学青年基金一项, 教育部博士点专项基金一项, 在研国家自然科学基金面上项目一项。

摘要:This paper analyzes an interest rate model with self-exciting jumps, in which ajump in the interest rate model increases the intensity of jumps in the samemodel. This self-exciting property leads to clustering effects in the interestrate model. We obtain a closed-form expression for the conditionalmoment-generating function when the model coefficients have affine structures.Based on the Girsanov-type measure transformation for general jump-diffusionprocesses, we derive the evolution of the interest rate under the equivalentmartingale measure and an explicit expression of the zero-coupon bond pricingformula. Furthermore, we give a pricing formula for the European call optionwritten on zero-coupon bonds. Finally, we provide an interpretation for theclustering effects in the interest rate model within a simple framework ofgeneral equilibrium. Indeed, we construct an interest rate model, theequilibrium state of which coincides with the interest rate model withclustering effects proposed in this paper。

时间：10月30日 10：00—11:00

报告三：

题目：ComparativeStatics in Risk Aversion and Portfolio Selection

报告人：夏建明研究员（中国科学院数学与系统科学研究院）

摘要: Thistalk has two parts: (1) Comparative statics of optimal portfolios for expectedutility maximizers in Black-Scholes market model; (2) Comparative risk aversionfor g-expected utility maximizers.  

时间：10月30日 11：00—12:00

地点：中央财经大学学术会堂南楼 506（中国精算研究院会议室）

欢迎各位老师和同学积极参加！