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英国帝国理工学院 Harry Zheng教授:Dynamic Portfolio Optimization with Looping Contagion Risk

(发布于:2017-04-05 )

主 题:Dynamic Portfolio Optimization with Looping Contagion Risk

主讲人:Harry Zheng教授

主持人:经济数学学院 马敬堂教授

时 间:2017年4月7日(星期五)下午1:00

地 点:通博楼B412

主办单位:经济数学学院  科研处

主讲人简介: Harry Zheng,英国帝国理工学院教授,Professor Zheng从事随机控制、金融数学领域研究,在Mathematics of Operations Research, SIAM Journal on Control and Optimization, Finance and Stochastics, SIAM Journal on Financial Mathematics, Journal of Economic Dynamics and Control, Quantitative Finance等top期刊(SCI或SSCI)发表数十篇论文。

内容提要:

We consider a dynamic portfolio optimization problem in a financial market with equities, credit derivatives and contagion risk. We introduce a new looping contagion model, assuming that the default intensity of one company depends on its counter party's stock price, while the default induces an immediate drop in its counter party's stock price. By separating the utility maximization problem into a pre-default and post-default component, we deduce two coupled HJB equations and show that the pre-default value function is the unique continuous constrained viscosity solution to the associated HJB equation. We obtain explicit solutions of value functions and trading strategies for investors with log utility, and show by a detailed numerical test that taking the contagion risk into account has a large impact to investor's optimal trading strategy. For power utility investors, we express the optimal trading strategy as the unique solution of an equation system and prove that the value function can be represented as the solution of a backward stochastic differential equation (joint work with Longjie Jia and Martijn Pistorius).


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