“れつきの臆病のせゐか、僕はあらゆる喜悦に不吉な予感を交へてゐた” ― 三島由紀夫

Computational Finance (2025)

Reference: Computational Finance, Christian Bayer, Antonis Papapantoleon, Raul Tempone

Ⅰ.Monte Carlo Simulation

Ⅱ.Quasi Monte Carlo Simulation

Ⅲ.Sample path generations

Ⅳ.Discretization of SDEs

Ⅴ.Fourier method for option pricing

Ⅵ.Numerical methods for PDEs

Mathematical Foundation of Machine Learning (2025)

Reference: Mathematische Grundlagen des Maschinellen Lernens I, Hanno Gottschalk

Ⅰ.Probability Framework

Ⅱ.Statistical Learning

Ⅲ.F-Divergence

Ⅳ.Divergence from Information Theory and Comparison of Topologies

Ⅴ.Empirical Risk Minimization

Ⅵ.Subgaussian rv & Rate of Learning

Ⅶ.Rate of Convergence in ERM Learning

Ⅷ.Concentration Inequalities

Ⅸ.PAC-Learning for Histograms

Ⅺ.Introduction to Supervised Learning

Numerical Method for ODEs (2025)

References: [1]. Numerische Mathematik II, Sandra May [2]. Numerik gewöhnlicher Differentialgleichungen, Rolf Rannacher

Ⅰ.Introduction

Ⅱ.Runge-Kutta Method

Ⅲ.Numerical Stability

Ⅳ.Linear Multistep Method

Ⅴ.Extrapolation

Ⅵ.Boundary Value Problem