Optimal Control: Applications in Risk Management and Online Markets

In this talk, directed at graduate students as well as current researchers in risk management and control theory, we present two problems for an agent to solve. The first is based on the seminal paper of Graversen, Peskir, and Shiryaev that solves the problem of predicting the ultimate maximum of a Brownian motion using adapted stopping times. We extend this to the model of measuring the ultimate risk associated with a toxic liability, which has applications in quantitative finance as well as insurance.

In the second problem, we model the actions of an agent within a network like Amazon or eBay, where she can balance maximizing her expected profit with managing her online reputation. This model employs techniques generally found in marketing campaigns, such as pulsing strategies.

Both problems employ standard techniques in one-dimensional optimal stopping and control, and it is of the opinion of the presenter that there are multiple possibilities for students and researchers to extend the models and results presented if interested.

References:

1.) Graversen, Svend Erik, Goran Peskir, and Albert Nikolaevich Shiryaev. "Stopping Brownian motion without anticipation as close as possible to its ultimate maximum." Theory of Probability & Its Applications 45.1 (2001):41-50.

2.) Cohen, Albert. "Examples of optimal prediction in the infinite horizon case." Statistics & probability letters 80.11 (2010): 950-957.

3.) Bradonjic, Milan and Cohen, Albert and Causley, Matthew, "An Infinite-Horizon Stochastic Optimal Control Model for Online Seller Behavior" (November 7, 2014). Available at SSRN: http://ssrn.com/abstract=2520608 or http://dx.doi.org/10.2139/ssrn.2520608. (Submitted to Risks, 2015.)