How Financial Engineering Can Help Cure COVID
We solve the problem of optimal treatment of an epidemic by using tools developed in financial engineering.
March 23, 2023 | 5PM - 6PM | Babbio Center Room 219
Zoom link: https://stevens.zoom.us/j/93855083404
We solve the problem of optimal treatment of an epidemic by using tools developed in financial engineering. More specifically, we develop an analogy between two problems: the optimal stochastic control of the SIR model in epidemiology, for the case of a risk-averse decision-maker, and the optimal portfolio problem, which we solve using the (now) well-known martingale method. The efficiency of the treatment follows an Ornstein-Uhlenbeck process.
We consider two different regimes of the stochastic SIR model. In the first regime the proportion of infected is very low, and the proportion of susceptible is very close to 100%. This problem corresponds to the problem of portfolio and consumption decision under mean-reverting returns, which was analyzed, among others, by Wachter (JFQA 2002). In the second regime, the proportion of infected is moderate, but not negligible. In that case, we found a perturbative solution. To our knowledge, this research represents one of the first attempts to develop analytical/perturbative solutions, as opposed to numerical solutions to stochastic SIR models.
The perturbative solution is analytically quite complicated. We will thus argue that determining this solution is (yet) completely out of reach of computers that would try (by brute search and machine differentiation) every possible analytical solution of the underlying Hamilton-Jacobi-Bellman equation. I hope this audience will find it refreshing news: humans can still beat the machine, in particular on this problem. This fact should contribute to motivate students to learn stochastic calculus. We will discuss some extensions of the model, for which perturbative solutions are likely to be found.
Finally, we compare the efficiency of our control to curb the COVID-19 epidemic to other types of control.
Henry Schellhorn is professor at the Institute of Mathematical Sciences at Claremont Graduate University. He is the current director of the financial engineering program. Previously, Henry was assistant professor of finance at the University of Lausanne, Switzerland, and held various positions in the finance industry, in both Switzerland and California. Henry’s current research areas include: stochastic analysis, mathematical finance, epidemiology, and traffic models, in particular the modelling of congestion pricing. Henry has been developing graduate courses at the cutting edge of the mathematical sciences, for instance stochastic partial differential equations, quantum computing, and machine learning for asset pricing. He has published in top-tier journals, including Management Science, Stochastic processes and Applications, Mathematical Biosciences, and the European Journal of Operational Research. Henry is an American and a Swiss citizen. He speaks French and English, plays the piano semi-professionally, and enjoys life with his wife Malina and his two children.