Tuesday, February 27, 2018 at 4:15pm
We present a tractable framework for model uncertainty, the so-called nonlinear Lévy processes, and use it to formulate and solve problems of robust utility maximization for an investor with logarithmic or power utility. The uncertainty is specified by a set of possible Lévy triplets; that is, possible instantaneous drift, volatility and jump characteristics of the price process. Thus, our setup describes uncertainty about drift, volatility and jumps over a class of fairly general models. We show that an optimal investment strategy exists and compute it in semi-closed form. Moreover, we provide a saddle point analysis describing a worst-case model.
The talk is based on joint works with Chong Liu and Marcel Nutz.
Ariel Neufeld is a postdoctoral researcher at the Department of Mathematics and RiskLab at ETH Zurich. In 2012, he started his Ph.D. in mathematics at Columbia University and ETH Zurich under the supervision of Professor Marcel Nutz (Columbia University) and Professor Martin Schweizer (ETH Zurich). He obtained his Ph.D. from ETH Zurich in 2015 for his thesis Knightian Uncertainty in Mathematical Finance.
His research focuses on stochastic optimal control applied to financial and insurance mathematics. In particular, he is interested in model uncertainty in financial markets and annuity contracts. Moreover, he studies machine learning algorithms, their convergence rates and their applications to finance and insurance.