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This volume includes the five lecture courses given at the CIME-EMS School on "Stochastic Methods in Finance" held in Bressanone/Brixen, Italy 2003. It deals with innovative methods, mainly from stochastic analysis, that play a fundamental role in the mathematical modelling of finance and insurance: the theory of stochastic processes, optimal and stochastic control, stochastic differential equations, convex analysis and duality theory. Five topics are treated in detail: Utility maximization in incomplete markets; the theory of nonlinear expectations and its relationship with the theory of risk measures in a dynamic setting; credit risk modelling; the interplay between finance and insurance; incomplete information in the context of economic equilibrium and insider trading.

Actuarial mathematics --- Finance --- Stochastic analysis --- Mathematical Theory --- Finance - General --- Mathematics --- Business & Economics --- Physical Sciences & Mathematics --- Mathematical models --- Stochastic analysis. --- Finances --- Analyse stochastique --- Mathematical models. --- Modèles mathématiques --- Probabilities. --- Public finance. --- Economics, Mathematical . --- Game theory. --- System theory. --- Probability Theory and Stochastic Processes. --- Public Economics. --- Quantitative Finance. --- Game Theory, Economics, Social and Behav. Sciences. --- Systems Theory, Control. --- Systems, Theory of --- Systems science --- Science --- Games, Theory of --- Theory of games --- Economics --- Mathematical economics --- Econometrics --- Cameralistics --- Public finance --- Public finances --- Currency question --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Philosophy --- Methodology

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These lecture notes by very authoritative scientists survey recent advances of mathematics driven by industrial application showing not only how mathematics is applied to industry but also how mathematics has drawn benefit from interaction with real-word problems. The famous David Report underlines that innovative high technology depends crucially for its development on innovation in mathematics. The speakers include three recent presidents of ECMI, one of ECCOMAS (in Europe) and the president of SIAM.

Mathematical models --- Mathematics --- Industrial applications --- Congresses --- Mathematics - Industrial applications - Congresses. --- Computer science—Mathematics. --- Calculus of variations. --- Numerical analysis. --- System theory. --- Probabilities. --- Thermodynamics. --- Mathematics of Computing. --- Calculus of Variations and Optimal Control; Optimization. --- Numerical Analysis. --- Systems Theory, Control. --- Probability Theory and Stochastic Processes. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Systems, Theory of --- Systems science --- Science --- Mathematical analysis --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Philosophy --- Mathematical models - Congresses.

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Nonholonomic systems are a widespread topic in several scientific and commercial domains, including robotics, locomotion and space exploration. This work sheds new light on this interdisciplinary character through the investigation of a variety of aspects coming from several disciplines. The main aim is to illustrate the idea that a better understanding of the geometric structures of mechanical systems unveils new and unknown aspects to them, and helps both analysis and design to solve standing problems and identify new challenges. In this way, separate areas of research such as Classical Mechanics, Differential Geometry, Numerical Analysis or Control Theory are brought together in this study of nonholonomic systems.

Nonholonomic dynamical systems. --- Geometry, Differential. --- Nonlinear control theory. --- Geometry, Differential --- Nonlinear control theory --- Nonholonomic dynamical systems --- Mathematical Theory --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Dynamics. --- Ergodic theory. --- Mechanics. --- Mechanics, Applied. --- System theory. --- Dynamical Systems and Ergodic Theory. --- Theoretical and Applied Mechanics. --- Systems Theory, Control. --- Systems, Theory of --- Systems science --- Science --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Philosophy

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System identification provides methods for the sensible approximation of real systems using a model set based on experimental input and output data. Tohru Katayama sets out an in-depth introduction to subspace methods for system identification in discrete-time linear systems thoroughly augmented with advanced and novel results. The text is structured into three parts. First, the mathematical preliminaries are dealt with: numerical linear algebra; system theory; stochastic processes; and Kalman filtering. The second part explains realization theory, particularly that based on the decomposition of Hankel matrices, as it is applied to subspace identification methods. Two stochastic realization results are included, one based on spectral factorization and Riccati equations, the other on canonical correlation analysis (CCA) for stationary processes. Part III uses the development of stochastic realization results, in the presence of exogenous inputs, to demonstrate the closed-loop application of subspace identification methods CCA and ORT (based on orthogonal decomposition). The addition of tutorial problems with solutions and Matlab® programs which demonstrate various aspects of the methods propounded to introductory and research material makes Subspace Methods for System Identification not only an excellent reference for researchers but also a very useful text for tutors and graduate students involved with courses in control and signal processing. The book can be used for self-study and will be of much interest to the applied scientist or engineer wishing to use advanced methods in modeling and identification of complex systems.

System identification. --- Stochastic analysis. --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Identification, System --- System analysis --- Telecommunication. --- System theory. --- Chemical engineering. --- Communications Engineering, Networks. --- Control and Systems Theory. --- Systems Theory, Control. --- Signal, Image and Speech Processing. --- Industrial Chemistry/Chemical Engineering. --- Chemistry, Industrial --- Engineering, Chemical --- Industrial chemistry --- Engineering --- Chemistry, Technical --- Metallurgy --- Electric communication --- Mass communication --- Telecom --- Telecommunication industry --- Telecommunications --- Communication --- Information theory --- Telecommuting --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Systems theory. --- Electrical engineering. --- Control engineering. --- Signal processing. --- Image processing. --- Speech processing systems. --- Electric engineering --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Computational linguistics --- Electronic systems --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication)

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299 G(t), and to obtain the corresponding properties of its Laplace transform (called the resolvent of - A) R(p) = (A + pl)-l , whose existence is linked with the spectrum of A. The functional space framework used will be, for simplicity, a Banach space(3). To summarise, we wish to extend definition (2) for bounded operators A, i.e. G(t) = exp( - tA) , to unbounded operators A over X, where X is now a Banach space. Plan of the Chapter We shall see in this chapter that this enterprise is possible, that it gives us in addition to what is demanded above, some supplementary information in a number of areas: - a new 'explicit' expression of the solution; - the regularity of the solution taking into account some conditions on the given data (u , u1,f etc ... ) with the notion of a strong solution; o - asymptotic properties of the solutions. In order to treat these problems we go through the following stages: in § 1, we shall study the principal properties of operators of semigroups {G(t)} acting in the space X, particularly the existence of an upper exponential bound (in t) of the norm of G(t). In §2, we shall study the functions u E X for which t --+ G(t)u is differentiable.

517.9 --- 517.5 --- 517.4 --- 51-7 --- 51-7 Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- 517.4 Functional determinants. Integral transforms. Operational calculus --- Functional determinants. Integral transforms. Operational calculus --- 517.5 Theory of functions --- Theory of functions --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Mathematical analysis. --- Numerical analysis. --- 517.984 --- 517.984 Spectral theory of linear operators --- Spectral theory of linear operators --- #KVIV:BB --- 519.6 --- 681.3 *G18 --- 681.3*G19 --- 681.3*G19 Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) --- Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- 519.63 --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Mathematical analysis --- Numerical analysis --- Analyse mathématique --- Analyse numérique --- Partial differential equations. --- Partial Differential Equations. --- Numerical Analysis. --- Partial differential equations --- Chemometrics. --- Computational intelligence. --- Applied mathematics. --- Engineering mathematics. --- Mathematical physics. --- Math. Applications in Chemistry. --- Computational Intelligence. --- Mathematical and Computational Engineering. --- Theoretical, Mathematical and Computational Physics. --- Physical mathematics --- Physics --- Engineering --- Engineering analysis --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Chemistry, Analytic --- Analytical chemistry --- Chemistry --- Mathematics --- Measurement --- Statistical methods --- System theory. --- Calculus of variations. --- Systems Theory, Control. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Mechanics. --- Classical Mechanics. --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Analysis (Mathematics). --- Analysis. --- 517.1 Mathematical analysis