SNAPSHOTS

Pedagogical Lectures

January to February 2018

From 23 to 25 January 2018, RMI hosted three consecutive pedagogical lectures by Prof. Halil Soner or ETH Zurich. This series of lectures titled, “Hedging-Pricing Duality” considered a more general financial market with Knightian uncertainty. Prof. Soner explained that although in such markets - by definition - there is no historical measure, the basic duality between hedging and pricing still holds. His lectures, which are based on his research, illustrated this connection by several convex duality results starting with simple discrete time models.

From 12 to 14 February 2018, Prof. Masaaki Kijima of Tokyo Metropolitan University hosted three pedagogical lectures on “An Expansion Approach for the Pricing of Exotic Options.” According to his current research, the talks presented a proposal of approximation method based on chaos expansion for pricing of European-style contingent claims, how to apply this method for the pricing of exotic options such as reciprocal options, volume-weighted-average-price (VWAP) options, and barrier options, and lastly he also considered a fractional volatility model and elaborated on how the expansion approach could be applied.

The third set of three-day pedagogical lectures was hosted by Prof. Nizar Touzi of Ecole Polytechnique. In the lecture series titled, “Continuous-Time Principal-Agent Problem,” Prof. Touzi stated that the Principal-Agent problem is the cornerstone for the modeling of optimal incentive schemes to account for moral hazard in economics and shared his research methodology for solving Stackelberg game problems in continuous time setting.

Research Seminar & Pedagogical Lectures

6, 19-21 March 2018

On 6 March 2018, Prof. Ulrich Horst of Humboldt University Berlin, gave a talk on “Mean Field Games with Singular Controls.” He explained that his research establishes the existence of relaxed solutions to mean field games (MFGs) with singular controls and prove approximations of solution results for a particular class of MFGs with singular controls by solutions; respectively control rules, for MFGs with purely regular controls. Prof. Horst explained that the existence and approximation results of this research strongly hinge on the use of the Skorokhod M1 topology on the space of cadlag functions. This talk was based on his joint work with Guanxing Fu.

Following the seminar Prof. Horst also gave three pedagogical lectures on, “Optimal Portfolio Liquidation and Stochastic Control with Singular State Constraints”, where he reviewed three approaches to solve stochastic control problems with singular terminal state constraints: the penalization method, an asymptotic expansion technique, and forward-backward SDEs with undetermined terminal value.

Research Seminar

3 April 2018

RMI invited A/P Dacheng Xiu from University of Chicago to host a research seminar on “Empirical Asset Pricing via Machine Learning.” A/P Xiu began the talk by explaining his research’s empirical set-up of cross section and time series stock return prediction and how he and his co-authors performed a comparative analysis of methods in the machine learning repertoire, including generalized linear models, dimension reduction, boosted regression trees, random forests, and neural networks. He further stated that they found that machine learning offers improved descriptions of asset price behavior, compared to traditional methods.