The slides shown at the event can be found here.

In our optimal portfolio asset allocation research, we take the perspective of a trader, who is allowed to trade in a risk-free bond, in stocks, and also in options, at a set of trading dates. In order to evaluate how satisfied the investor is with the return, an objective function is used. A high quality objective function is able to numerically represent the investor’s preferences of how much risk is acceptable for a certain level of potential profit. Moreover, we introduce market frictions aspects of incomplete markets and trading constraints. Regarding the market, we add transaction costs as well as a non-bankruptcy constraint and for the trading strategies, we introduce leverage constraints. The resulting optimization problem admits for closed form strategies only in rare cases and we therefore have to rely on numerical approximations. The discrete counterpart (in time and/or in probability space) is then approximated by letting deep neural networks represent the trading strategies and optimizing with a gradient decent type algorithm. A general framework results, where we can invest in multiple assets, and deal with quite general objective functions.

Prof.dr.ir Cornelis (“Kees”) Oosterlee, Chair of financial Mathematics, Mathematical Institute, Utrecht University. Prof. Oosterlee has been working on computational problems in financial mathematics since 2000. He is co-author of two textbooks (“Multigrid” 2001, and “Mathematical Modeling and Computation in Finance”, 2019), and many scientific publications. Financial derivative pricing and risk management methods he co-developed include the COS method on Fourier cosine expansions, SWIFT (Shannon Wavelet Inverse Fourier Transform method), SGBM (Stochastic Grid Bundling Method), SCMC (Stochastic Collocation Monte Carlo Method), and the Seven-League scheme (7L). Machine learning in Finance is another research interest in Oosterlee’s group, where he works on optimal portfolio selection, time series and anomaly detection methods. Oosterlee has led two EU projects on risk management in finance and insurance, in collaboration with the industry, and he also worked on several Dutch national projects. He has been a guest lecturer at Oxford Uni, UK, Hitotsubashi Uni., Japan, Uni. A Coruna Spain, amongst others.