主 讲  人： Stevens Institute of Technology, 崔振嵛副教授

报告时间：2023年6月7日（星期三）上午10：00—11：00

报告地点：腾讯会议：725-560-567

报告摘要:

In this talk, I discuss three recent research streams of mine: continuous-time Markov chain (CTMC) approximation,  Delta family method, and diffusion operator integral (DOI) method. I choose the common topic of stochastic control to illustrate the three methods, although they have much wider applications in contextual areßas. In particular,  I shall discuss three alternative methods to solve stochastic control problems arising in utility maximization in financial decision making, e.g. Merton problem.

The first method is based on the continuous-time Markov chain approximation of the underlying (uncontrolled) asset price process (modeled as diffusions), and extends the Kushner-Dupuis DTMC approximation method.

The second method is the Dirac Delta family method developed by the author. The main idea is to directly start from the dynamical programming equation and compute the conditional expectation using a novel representation of the conditional density function through the Dirac Delta function and the corresponding series representation. We obtain an explicit series representation of the value function, whose coefficients are expressed through integration of the value function at a later time point against a chosen basis function. Thus we are able to set up a recursive integration time-stepping scheme to compute the optimal value function given the known terminal condition, e.g. utility function.

The third method is based on my ongoing research on the diffusion operator integral (DOI) method, which originates from Heath and Platen (2002) in Monte Carlo simulation. We apply it to solve the Merton problem under general Markovian models, by expanding the value function around known closed-form value functions under the Black-Scholes model, and providing explicit recursion formulae for all higher order correction terms.

Numerical examples are provided for the Merton problem under representative stochastic local volatility models, e.g. Heston, SABR, etc. We benchmark against known results in the literature and showcase the advantages of the proposed methods.

主讲人简介：

崔振嵛，理学博士，Stevens Institute of Technology 商学院副教授，博士生导师，博士毕业于University of Waterloo，现任International Journal of Finance and Economics 副主编。主要研究兴趣有金融工程，随机模拟，及金融科技，在 Econometric Theory, Mathematical Finance, INFORMS Journal on Computing, Journal of Financial Econometrics, European Journal of Operational Research 等杂志发表数十篇论文。目前主持 NSF CNS-2113906: “Fast Quantum Method for Financial Risk Measurement” 科研项目。