International Conference «Advanced Mathematics, Computations and Applications 2019» (AMCA-2019)

Novosibirsk, Russia

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Open lecture

COMPUTATIONAL CHALLENGES IN MATHEMATICAL FINANCE

Makarov Roman, Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada

wednesday July 3, 2019 from 15:00 till 18:30

room 3107 of the new building of NSU

In this series of mini-lectures, we discuss four main areas of quantitative finance related to asset price modelling, derivative valuation, portfolio optimization, and risk management. First, we consider several classes of stochastic models for asset prices that are based on diffusion and Levy processes. We examine issues related to modelling stochastic volatility and jumps, multiscale dynamics, and coupled systems. The second theme relates to valuation of derivatives such as options using Monte Carlo and other computational techniques. We look into computational challenges related to pricing multi-asset products and path-dependent derivatives. Third, we review the mean-variance portfolio optimization theory and how to find an optimal allocation strategy by solving the Hamilton-Jacobi-Bellman equation. Finally, we study several credit risk models, as well as systemic risk models of a banking network.