This book presents a collection of recent advances in stochastic numerical analysis and computational finance. Stochastic numerical methods have played a pivotal role in probability theory, statistics, and applied mathematics, particularly in the rapidly evolving fields of machine learning and data science. They have also achieved significant success in computational finance. The volume highlights cutting-edge developments in numerical techniques for stochastic differential equations and stochastic models in finance. This collection offers valuable insights for researchers and practitioners seeking to deepen their understanding of stochastic modeling and its applications in finance and beyond.

Provides new numerical schemes and algorithms ensured by theoretical results Includes machine learning and deep learning methods in finance Covers various financial models important both in theory and practice

Autorentext

Jiro Akahori is a professor of Graduate School of Mathematical Sciences at Ritsumeikan University.

Syoiti Ninomiya is a professor of Department of Mathematics, Institute of Science Tokyo.

Toshihiro Yamada is a professor of Graduate School of Economics at Hitotsubashi University.

Inhalt

Chapter 1 Policy improvement algorithm for an optimal consumption and investment problem under a certain nonlinear stochastic factor model.- Chapter 2 An extended Milstein scheme for effective weak approximation of diffusions.- Chapter 3 Expansion of Bermudan option price using deep learning.- Chapter 4 Approximation for stochastic PDES and the HJM Model.- Chapter 5 On a Prolongation of the Nonlinear Stochastic Asymptotic Expansion of the Solution of a Semilinear PDE.