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While the original works on Malliavin calculus aimed to study the smoothness of densities of solutions to stochastic differential equations, this book has another goal. It portrays the most important and innovative applications in stochastic control and finance, such as hedging in complete and incomplete markets, optimisation in the presence of asymmetric information and also pricing and sensitivity analysis. In a self-contained fashion, both the Malliavin calculus with respect to Brownian motion and general Lévy type of noise are treated. Besides, forward integration is included and indeed extended to general Lévy processes. The forward integration is a recent development within anticipative stochastic calculus that, together with the Malliavin calculus, provides new methods for the study of insider trading problems. To allow more flexibility in the treatment of the mathematical tools, the generalization of Malliavin calculus to the white noise framework is also discussed. This book is a valuable resource for graduate students, lecturers in stochastic analysis and applied researchers.

Electronic books. -- local. --- Lévy processes. --- Malliavin calculus. --- Malliavin calculus --- Lâevy processes --- Mathematical Statistics --- Mathematics --- Physical Sciences & Mathematics --- Calculus, Malliavin --- Mathematics. --- Economics, Mathematical. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Stochastic analysis --- Random walks (Mathematics) --- Distribution (Probability theory. --- Finance. --- Funding --- Funds --- Economics --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology

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These Proceedings offer a selection of peer-reviewed research and survey papers by some of the foremost international researchers in the fields of finance, energy, stochastics and risk, who present their latest findings on topical problems. The papers cover the areas of stochastic modeling in energy and financial markets; risk management with environmental factors from a stochastic control perspective; and valuation and hedging of derivatives in markets dominated by renewables, all of which further develop the theory of stochastic analysis and mathematical finance. The papers were presented at the first conference on “Stochastics of Environmental and Financial Economics (SEFE)”, being part of the activity in the SEFE research group of the Centre of Advanced Study (CAS) at the Academy of Sciences in Oslo, Norway during the 2014/2015 academic year.

Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Mathematics. --- Partial differential equations. --- Game theory. --- System theory. --- Calculus of variations. --- Probabilities. --- Environmental economics. --- Systems Theory, Control. --- Probability Theory and Stochastic Processes. --- Environmental Economics. --- Game Theory, Economics, Social and Behav. Sciences. --- Partial Differential Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Economics --- Environmental quality --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Systems, Theory of --- Systems science --- Science --- Games, Theory of --- Theory of games --- Mathematical models --- Partial differential equations --- Math --- Environmental aspects --- Economic aspects --- Philosophy --- Distribution (Probability theory. --- Differential equations, partial. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Systems theory. --- Systems Theory --- Control

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This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blend of topics gives an overview of the frontiers of mathematics for finance. New results, new methods and new models are all introduced in different forms according to the subject. Additionally, the existing literature on the topic is reviewed. The diversity of the topics makes the book suitable for graduate students, researchers and practitioners in the areas of financial modeling and quantitative finance. The chapters will also be of interest to experts in the financial market interested in new methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance.

Macroeconomics --- Quantitative methods (economics) --- Economics --- Operational research. Game theory --- Mathematical statistics --- Financial analysis --- Business economics --- stochastische analyse --- economie --- statistiek --- macro-economie --- financiële analyse --- econometrie --- kansrekening

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Kiyosi Ito, the founder of stochastic calculus, is one of the few central figures of the twentieth century mathematics who reshaped the mathematical world. Today stochastic calculus is a central research field with applications in several other mathematical disciplines, for example physics, engineering, biology, economics and finance. The Abel Symposium 2005 was organized as a tribute to the work of Kiyosi Ito on the occasion of his 90th birthday. Distinguished researchers from all over the world were invited to present the newest developments within the exciting and fast growing field of stochastic analysis. The present volume combines both papers from the invited speakers and contributions by the presenting lecturers. A special feature is the Memoirs that Kiyoshi Ito wrote for this occasion. These are valuable pages for both young and established researchers in the field.

Stochastic analysis --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Distribution (Probability theory. --- Mathematics. --- Global analysis (Mathematics). --- Mathematical statistics. --- Finance. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Real Functions. --- Analysis. --- Statistical Theory and Methods. --- Quantitative Finance. --- Funding --- Funds --- Economics --- Currency question --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistical methods --- Probabilities. --- Applied mathematics. --- Engineering mathematics. --- Functions of real variables. --- Analysis (Mathematics). --- Statistics . --- Economics, Mathematical . --- Real variables --- Engineering --- Engineering analysis --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Mathematical economics --- Econometrics --- Statistical analysis --- Statistical data --- Statistical science --- Methodology --- Itō, Kiyosi, --- Itō, K. --- Ito, Kiesi, --- Itō, Kiyoshi, --- 伊藤淸, --- 伊藤清,

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The Abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.

Group theory --- Differential equations --- Mathematics --- Applied physical engineering --- Engineering sciences. Technology --- Computer science --- Computer. Automation --- differentiaalvergelijkingen --- informatica --- externe fixatie (geneeskunde --- systeemtheorie --- wiskunde --- systeembeheer --- ingenieurswetenschappen