Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This textbook provides a self-contained introduction to numerical methods in probability with a focus on applications to finance. Topics covered include the Monte Carlo simulation (including simulation of random variables, variance reduction, quasi-Monte Carlo simulation, and more recent developments such as the multilevel paradigm), stochastic optimization and approximation, discretization schemes of stochastic differential equations, as well as optimal quantization methods. The author further presents detailed applications to numerical aspects of pricing and hedging of financial derivatives, risk measures (such as value-at-risk and conditional value-at-risk), implicitation of parameters, and calibration. Aimed at graduate students and advanced undergraduate students, this book contains useful examples and over 150 exercises, making it suitable for self-study.

Mathematics. --- Economics, Mathematical. --- Probabilities. --- Statistics. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Economics --- Mathematical economics --- Math --- Science --- Methodology --- Distribution (Probability theory. --- Finance. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Funding --- Funds --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Economics, Mathematical . --- Statistics .

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Calcul intégral. --- Convolutions (mathématiques) --- Fourier, Transformations de. --- Topologie. --- Riemann, Intégrale de. --- Mesure, Théorie de la. --- Calculus, Integral --- Convolutions (Mathematics) --- Fourier transformations --- Topology --- Measure theory --- Transformations de Fourier --- Topologie --- Théorie de la mesure

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Vector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science. In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach space—a unique feature of its content. Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees. While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.

Probabilities. --- Telecommunication. --- Mathematics --- Probability Theory. --- Communications Engineering, Networks. --- Computational Mathematics and Numerical Analysis. --- Data processing. --- Probabilitats

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Operational research. Game theory --- Probability theory --- Mathematics --- Telecommunication technology --- Mass communications --- Computer. Automation --- waarschijnlijkheidstheorie --- stochastische analyse --- informatica --- tekstverwerking --- wiskunde --- kansrekening --- communicatietechnologie