# model uncertainty

Tuesday, April 24, 2018 - 1:00pm - 1:30pm

Oksana Chkrebtii (The Ohio State University)

When computational constraints prohibit model evaluation at all but a small number of parameter settings, a dimension-reduced emulator of the system can be constructed and interrogated at arbitrary parameter regimes. Existing approaches to emulation consider models with deterministic output. However, in many cases the underlying mathematical model, or the simulator approximating the mathematical model, are stochastic. We propose a Bayesian calibration approach for stochastic simulators.

Tuesday, June 12, 2018 - 9:00am - 9:50am

Bernt Oksendal (University of Oslo)

We consider the problem of optimal control of a mean-field stochastic differential equation (SDE) under model uncertainty. The model uncertainty is represented by ambiguity about the law L(X(t)) of the state X(t) at time t. For example, it could be the law L_P(X(t)) of X(t) with respect to the given, underlying probability measure P. This is the classical case when there is no model uncertainty. But it could also be the law L_Q(X(t)) with respect to some other probability measure Q or, more generally, any random measure \mu(t) on R with total mass 1.

Wednesday, June 13, 2018 - 10:00am - 10:50am

Huyen Pham (Université de Paris VII (Denis Diderot))

This talk is concerned with multi-asset mean-variance portfolio selection problem under model uncertainty.

We develop a continuous time framework for taking into account ambiguity aversion about both expected rate of return and correlation matrix of stocks, and for studying the effects on portfolio diversification.

We develop a continuous time framework for taking into account ambiguity aversion about both expected rate of return and correlation matrix of stocks, and for studying the effects on portfolio diversification.

Monday, May 7, 2018 - 11:00am - 11:50am

Hideo Nagai (Kansai University)

Suppose that we are given a semi-martngale whose coefficients are affected by a diffusion process and a control parameter. We are concerned with minimizing the probability that the growth rate of the semi-martingale falls below a certain level over large time. It is to be noted that the asymptotic behavior of the minimizing probability relates to risk-sensitive stochastic control in the risk-averse case.