Nicolas Privault Boeken

This book provides an undergraduate introduction to discrete and continuous- time Markov chains and their applications. It includes more than 70 exercises, along with complete solutions, that help illustrate and present all concepts.

Focusing on stochastic interest rate modeling, this book provides a detailed, step-by-step approach to understanding and calculating various interest rates, including short rates and forward rates like LIBOR and swap rates within the HJM and BGM frameworks. It covers the pricing and hedging of derivatives such as bond options, caps, and swaptions using forward measure techniques. Additionally, it introduces concepts of default bond pricing and model calibration, making it a comprehensive resource for those interested in financial mathematics and derivative pricing.

Focusing on discrete-time stochastic processes, the text explores random interactions and algorithms centered on the Markov property. It delves into topics such as random walks, Markov chain convergence, and phase-type distributions, with practical applications in search engines and probabilistic automata. The introduction of the Ising model highlights its relevance in statistical physics. Additionally, it addresses data science applications through hidden Markov models and decision processes. The book includes 32 exercises and 17 detailed problems, enhancing understanding of statistical learning concepts.

Focusing on interest rate modeling and derivative pricing, this book offers a clear and structured introduction to essential concepts in financial mathematics and risk management. It features explicit calculations and includes exercises with complete solutions, catering to advanced undergraduate and graduate students. The revised second edition adds a new chapter on credit risk and covers a range of stochastic interest rate models, from standard short rate to forward rate models, alongside advanced topics like the BGM model and its calibration.

Focusing on the fundamentals of Markov chains, this book serves as an undergraduate introduction to both discrete and continuous-time models. It emphasizes practical applications and features over 70 exercises with complete solutions, aiding in the understanding of key concepts and enhancing learning through practice.

This monograph is an introduction to some aspects of stochastic analysis in the framework of normal martingales, in both discrete and continuous time. The text is mostly self-contained, except for Section 5.7 that requires some background in geometry, and should be accessible to graduate students and researchers having already received a basic training in probability. Prereq- sites are mostly limited to a knowledge of measure theory and probability, namely?-algebras, expectations, andconditionalexpectations. Ashortint- duction to stochastic calculus for continuous and jump processes is given in Chapter 2 using normal martingales, whose predictable quadratic variation is the Lebesgue measure. There already exists several books devoted to stochastic analysis for c- tinuous di? usion processes on Gaussian and Wiener spaces, cf. e. g. [51], [63], [65], [72], [83], [84], [92], [128], [134], [143], [146], [147]. The particular f- ture of this text is to simultaneously consider continuous processes and jump processes in the uni? ed framework of normal martingales.