讲座题目：Optimal Risk and Dynamic Pricing Management for a Capacity Allocation Problem
主讲人： 李迅 授课
主持人： 艾兴政 授课
Using a real-options approach, we derive dynamically optimal capacity management strategies for selling a perishable underlying good in the presence of an exogenous benchmark market. The good generally refers to a commodity product that is costly to store and pinpoint to deliver. Taking into account how the competition effects in a market influence the demand process for the underlying good, we show analytically that when the market risk is hedged by a European put option and with the purchase of the put, the maximal revenue of the remaining quantity of the good (or, the service capacity) is attained by a dynamic allocation policy in line with the benchmark market price. In addition to showing that the maximal revenue margin of the unsold underlying good decreases in its remaining quantity, and that the optimal premium diminishes on average, as the end of the selling horizon approaches, we establish more general structural properties of this optimal capacity allocating policy to characterize the marginal capacity with the option's strike price, initial capacity and starting benchmark price. Numerical results in the context of selling shipping capacity further illustrate how the particular properties can be used to optimize a put option hedge and a risk-adjusted revenue-maximization strategy.
Xun Li received his Ph.D. degree in 2000 from Department of Systems Engineering and Engineering Management at the Chinese University of Hong Kong, and he stayed with the same department as a postdoctoral research fellow until 2001. From 2001 to 2003, he was a postdoctoral fellow in the Mathematical and Computational Finance Laboratory at University of Calgary. From 2003 to 2007, he was a visiting fellow (equivalent to research assistant professor) in the Department of Mathematics at the National University of Singapore. He joined the Department of Applied Mathematics at the Hong Kong Polytechnic University as Assistant Professor in August 2007, serves as Associate Professor in July 2013 and will become Professor in July 2019. His main research areas are stochastic control and applied probability with financial applications, and he has published in journals such as SIAM Journal on Control and Optimization, Annals of Applied Probability, IEEE Transactions on Automatic Control, Automatica, Mathematical Finance, Annals of Finance and Quantitative Finance.