Asymptotic analysis of stochastic stock price models is the central topic of the present volume. Special examples of such models are stochastic volatility models, that have been developed as an answer to certain imperfections in a celebrated Black-Scholes model of option pricing. In a stock price model with stochastic volatility, the random behavior of the volatility is described by a stochastic process. For instance, in the Hull-White model the volatility process is a geometric Brownian motion, the Stein-Stein model uses an Ornstein-Uhlenbeck process as the stochastic volatility, and in the Heston model a Cox-Ingersoll-Ross process governs the behavior of the volatility. One of the author's main goals is to provide sharp asymptotic formulas with error estimates for distribution densities of stock prices, option pricing functions, and implied volatilities in various stochastic volatility models. The author also establishes sharp asymptotic formulas for the implied volatility at extreme strikes in general stochastic stock price models. The present volume is addressed to researchers and graduate students working in the area of financial mathematics, analysis, or probability theory. The reader is expected to be familiar with elements of classical analysis, stochastic analysis and probability theory.

The modern financial industry has been required to deal with large and diverse portfolios in a variety of asset classes often with limited market data available. Financial Signal Processing and Machine Learning unifies a number of recent advances made in signal processing and machine learning for the design and management of investment portfolios and financial engineering. This book bridges the gap between these disciplines, offering the latest information on key topics including characterizing statistical dependence and correlation in high dimensions, constructing effective and robust risk measures, and their use in portfolio optimization and rebalancing. The book focuses on signal processing approaches to model return, momentum, and mean reversion, addressing theoretical and implementation aspects. It highlights the connections between portfolio theory, sparse learning and compressed sensing, sparse eigen-portfolios, robust optimization, non-Gaussian data-driven risk measures, graphical models, causal analysis through temporal-causal modeling, and large-scale copula-based approaches. Key features: Highlights signal processing and machine learning as key approaches to quantitative finance. Offers advanced mathematical tools for high-dimensional portfolio construction, monitoring, and post-trade analysis problems. Presents portfolio theory, sparse learning and compressed sensing, sparsity methods for investment portfolios. including eigen-portfolios, model return, momentum, mean reversion and non-Gaussian data-driven risk measures with real-world applications of these techniques. Includes contributions from leading researchers and practitioners in both the signal and information processing communities, and the quantitative finance community.

This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie’s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.

This book is a comprehensive exploration of the interplay between Stochastic Analysis, Geometry, and Partial Differential Equations (PDEs). It aims to investigate the influence of geometry on diffusions induced by underlying structures, such as Riemannian or sub-Riemannian geometries, and examine the implications for solving problems in PDEs, mathematical finance, and related fields. The book aims to unify the relationships between PDEs, nonholonomic geometry, and stochastic processes, focusing on a specific condition shared by these areas known as the bracket-generating condition or Hörmander's condition. The main objectives of the book are:The intended audience for this book includes researchers and practitioners in mathematics, physics, and engineering, who are interested in stochastic techniques applied to geometry and PDEs, as well as their applications in mathematical finance and electrical circuits.

What distinguishes this book from other texts on mathematical finance is the use of both probabilistic and PDEs tools to price derivatives for both constant and stochastic volatility models, by which the reader has the advantage of computing explicitly a large number of prices for European, American and Asian derivatives.The book presents continuous time models for financial markets, starting from classical models such as Black-Scholes and evolving towards the most popular models today such as Heston and VAR.A key feature of the textbook is the large number of exercises, mostly solved, which are designed to help the reader to understand the material.The book is based on the author's lectures on topics on computational finance for senior and graduate students, delivered in USA (Princeton University and EMU), Taiwan and Kuwait. The prerequisites are an introductory course in stochastic calculus, as well as the usual calculus sequence.The book is addressed to undergraduate and graduate students in Masters of Finance programs as well as to those who wish to become more efficient in their practical applications.Topics covered:

This book is the outcome of the CIMPA School on Statistical Methods and Applications in Insurance and Finance, held in Marrakech and Kelaat M'gouna (Morocco) in April 2013. It presents two lectures and seven refereed papers from the school, offering the reader important insights into key topics. The first of the lectures, by Frederic Viens, addresses risk management via hedging in discrete and continuous time, while the second, by Boualem Djehiche, reviews statistical estimation methods applied to life and disability insurance. The refereed papers offer diverse perspectives and extensive discussions on subjects including optimal control, financial modeling using stochastic differential equations, pricing and hedging of financial derivatives, and sensitivity analysis. Each chapter of the volume includes a comprehensive bibliography to promote further research.

This book introduces multi-objective design methods to solve multi-objective optimization problems (MOPs) of linear/nonlinear dynamic systems under intrinsic random fluctuation and external disturbance. The MOPs of multiple targets for systems are all transformed into equivalent linear matrix inequality (LMI)-constrained MOPs. Corresponding reverse-order LMI-constrained multi-objective evolution algorithms are introduced to solve LMI-constrained MOPs using MATLAB®. All proposed design methods are based on rigorous theoretical results, and their applications are focused on more practical engineering design examples. Features: Discusses multi-objective optimization from an engineer’s perspective. Contains the theoretical design methods of multi-objective optimization schemes. Includes a wide spectrum of recent research topics in control design, especially for stochastic mean field diffusion problems. Covers practical applications in each chapter, like missile guidance design, economic and financial systems, power control tracking, minimization design in communication, and so forth. Explores practical multi-objective optimization design examples in control, signal processing, communication, and cyber-financial systems. This book is aimed at researchers and graduate students in electrical engineering, control design, and optimization.

Computational finance is an interdisciplinary field which joins financial mathematics, stochastics, numerics and scientific computing. Its task is to estimate as accurately and efficiently as possible the risks that financial instruments generate. This volume consists of a series of cutting-edge surveys of recent developments in the field written by leading international experts. These make the subject accessible to a wide readership in academia and financial businesses. The book consists of 13 chapters divided into 3 parts: foundations, algorithms and applications. Besides surveys of existing results, the book contains many new previously unpublished results.

R Programming for Actuarial Science Professional resource providing an introduction to R coding for actuarial and financial mathematics applications, with real-life examples R Programming for Actuarial Science provides a grounding in R programming applied to the mathematical and statistical methods that are of relevance for actuarial work. In R Programming for Actuarial Science, readers will find: Basic theory for each chapter to complement other actuarial textbooks which provide foundational theory in depth. Topics covered include compound interest, statistical inference, asset-liability matching, time series, loss distributions, contingencies, mortality models, and option pricing plus many more typically covered in university courses. More than 400 coding examples and exercises, most with solutions, to enable students to gain a better understanding of underlying mathematical and statistical principles. An overall basic to intermediate level of coverage in respect of numerous actuarial applications, and real-life examples included with every topic. Providing a highly useful combination of practical discussion and basic theory, R Programming for Actuarial Science is an essential reference for BSc/MSc students in actuarial science, trainee actuaries studying privately, and qualified actuaries with little programming experience, along with undergraduate students studying finance, business, and economics.

This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.