讲座人介绍：

Henry Schellhorn is professor of mathematics at Claremont Graduate University’s Institute of Mathematics Sciences, director of the Institute of Mathematical Sciences, and academic director of the Financial Engineering Program at the Drucker School of Management. His research focuses in the areas of Monte Carlo simulation, credit risk management, interest rate models, queuing theory, and combinatorial auctions.

Since the seminal work of Black Scholes (1973), there has been a flurry of results in option pricing that exploited the now well-established rules of stochastic calculus. We explore in this talk the applications to option pricing of two relatively unknown results of stochastic analysis: (i) the Ito-Wentzell formula, and (ii) Dyson series.  We apply the Ito-Wentzell formula to financial liquidity models and to a traffic model. Several financial liquidity models show that illiquidity has little or no impact on option pricing; various authors have given different explanation of this counterintuitive fact; our explanation is that these liquidity models are generically unstable. For traffic, we consider an application of financial engineering to congestion pricing on a road with autonomous (self-driving) cars. In the second part of the talk, we show several applications of Dyson series to the pricing of financial options: call option pricing in the SABR model, and bond pricing in the Cox-Ingersoll-model where the underlying process is (1) Brownian motion (2) fractional Brownian motion and (3) a general Levy process.