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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.

Business mathematics. --- Finance -- Mathematical methods. --- Finance -- Mathematical models. --- Business & Economics --- Economic Theory --- Finance --- Mathematical models. --- Mathematics. --- Economics, Mathematical. --- Probabilities. --- Sociophysics. --- Econophysics. --- Statistics. --- Macroeconomics. --- Quantitative Finance. --- Probability Theory and Stochastic Processes. --- Macroeconomics/Monetary Economics//Financial Economics. --- Socio- and Econophysics, Population and Evolutionary Models. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Finance. --- Distribution (Probability theory. --- Data-driven Science, Modeling and Theory Building. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Economics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Funding --- Funds --- Currency question --- Economics, Mathematical . --- Statistics . --- Statistical physics --- Mathematical sociology --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Mathematical economics --- 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.

Economics --- Functional analysis --- Partial differential equations --- Numerical methods of optimisation --- Operational research. Game theory --- Probability theory --- Mathematics --- Environmental protection. Environmental technology --- Engineering sciences. Technology --- Recreation. Games. Sports. Corp. expression --- differentiaalvergelijkingen --- analyse (wiskunde) --- waarschijnlijkheidstheorie --- stochastische analyse --- economie --- spellen --- systeemtheorie --- milieuzorg --- speltheorie --- wiskunde --- systeembeheer --- kansrekening --- optimalisatie

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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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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.

Combinatorial analysis --- Computer science --- Differential Equations. --- Mathematics. --- Systems theory. --- Group theory. --- Computational Mathematics and Numerical Analysis. --- Ordinary Differential Equations. --- Approximations and Expansions. --- Systems Theory, Control. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Math --- Science --- 517.91 Differential equations --- Differential equations --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics --- Computer mathematics. --- Differential equations. --- Approximation theory. --- System theory. --- Systems, Theory of --- Systems science --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Philosophy --- Control theory. --- Systems Theory, Control . --- Data processing. --- Dynamics --- Machine theory