Risk and financial management : mathematical and computational methods / / Charles Tapiero

• Record Nr.: UNINA9911019822603321
• Autore: Tapiero Charles S
• Pubbl/distr/stampa: Chichester, West Sussex ; ; Hoboken, NJ, : John Wiley, c2004
• ISBN: 9780470020350; 9786610541577; 9781280541575; 1280541571; 9780470020357; 0470020350; 9780470020364; 0470020369
• Descrizione fisica: 1 online resource (359 p.)
• Disciplina: 658.15/5/015192
• Soggetti: Finance - Mathematical models; Risk management
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Risk and Financial Management; Contents; Preface; Part I: Finance and Risk Management; Chapter 1 Potpourri; 1.1 Introduction; 1.2 Theoretical finance and decision making; 1.3 Insurance and actuarial science; 1.4 Uncertainty and risk in finance; 1.4.1 Foreign exchange risk; 1.4.2 Currency risk; 1.4.3 Credit risk; 1.4.4 Other risks; 1.5 Financial physics; Selected introductory reading; Chapter 2 Making Economic Decisions under Uncertainty; 2.1 Decision makers and rationality; 2.1.1 The principles of rationality and bounded rationality; 2.2 Bayes decision making; 2.2.1 Risk management; 2.3 Decision criteria 2.3.1 The expected value (or Bayes) criterion; 2.3.2 Principle of (Laplace) insufficient reason; 2.3.3 The minimax (maximin) criterion; 2.3.4 The maximax (minimin) criterion; 2.3.5 The minimax regret or Savage's regret criterion; 2.4 Decision tables and scenario analysis; 2.4.1 The opportunity loss table; 2.5 EMV, EOL, EPPI, EVPI; 2.5.1 The deterministic analysis; 2.5.2 The probabilistic analysis; ; Selected references and readings; Chapter 3 Expected Utility; 3.1 The concept of utility; 3.1.1 Lotteries and utility functions; 3.2 Utility and risk behaviour; 3.2.1 Risk aversion 3.2.2 Expected utility bounds; 3.2.3 Some utility functions; 3.2.4 Risk sharing; 3.3 Insurance, risk management and expected utility; 3.3.1 Insurance and premium payments; 3.4 Critiques of expected utility theory; 3.4.1 Bernoulli, Buffon, Cramer and Feller; 3.4.2 Allais Paradox; 3.5 Expected utility and finance; 3.5.1 Traditional valuation; 3.5.2 Individual investment and consumption; 3.5.3 Investment and the CAPM; 3.5.4 Portfolio and utility maximization in practice; 3.5.5 Capital markets and the CAPM again; 3.5.6 Stochastic discount factor, assets pricing and the Euler equation 3.6 Information asymmetry; 3.6.1 'The lemon phenomenon' or adverse selection; 3.6.2 'The moral hazard problem'; 3.6.3 Examples of moral hazard; 3.6.4 Signalling and screening; 3.6.5 The principal-agent problem; References and further reading; Chapter 4 Probability and Finance; 4.1 Introduction; 4.2 Uncertainty, games of chance and martingales; 4.3 Uncertainty, random walks and stochastic processes; 4.3.1 The random walk; 4.3.2 Properties of stochastic processes; 4.4 Stochastic calculus; 4.4.1 Ito's Lemma; 4.5 Applications of Ito's Lemma 4.5.1 Applications; 4.5.2 Time discretization of continuous-time finance models; 4.5.3 The Girsanov Theorem and martingales*; References and further reading; Chapter 5 Derivatives Finance; 5.1 Equilibrium valuation and rational expectations; 5.2 Financial instruments; 5.2.1 Forward and futures contracts; 5.2.2 Options; 5.3 Hedging and institutions; 5.3.1 Hedging and hedge funds; 5.3.2 Other hedge funds and investment strategies; 5.3.3 Investor protection rules; References and additional reading; Part II: Mathematical and Computational Finance; Chapter 6 Options and Derivatives Finance Mathematics
• Sommario/riassunto: Financial risk management has become a popular practice amongst financial institutions to protect against the adverse effects of uncertainty caused by fluctuations in interest rates, exchange rates, commodity prices, and equity prices. New financial instruments and mathematical techniques are continuously developed and introduced in financial practice. These techniques are being used by an increasing number of firms, traders and financial risk managers across various industries. Risk and Financial Management: Mathematical and Computational Methods confronts the many issues and controver

Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs / / by Dinh Dũng, Van Kien Nguyen, Christoph Schwab, Jakob Zech

• Record Nr.: UNINA9910751387703321
• Autore: Dũng Dinh
• Pubbl/distr/stampa: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023
• ISBN: 9783031383847
• Edizione: [1st ed. 2023.]
• Descrizione fisica: 1 online resource (216 pages)
• Collana: Lecture Notes in Mathematics, , 1617-9692 ; ; 2334
• Altri autori (Persone): NguyenVan Kien; SchwabChristoph; ZechJakob
• Disciplina: 515.35
• Soggetti: Differential equations; Probabilities; Numerical analysis; Functional analysis; Differential Equations; Probability Theory; Numerical Analysis; Functional Analysis
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Preface -- Acknowledgement -- Contents -- List of Symbols -- List of Abbreviations -- 1 Introduction -- 1.1 An Example -- 1.2 Contributions -- 1.3 Scope of Results -- 1.4 Structure and Content of This Text -- 1.5 Notation and Conventions -- 2 Preliminaries -- 2.1 Finite Dimensional Gaussian Measures -- 2.1.1 Univariate Gaussian Measures -- 2.1.2 Multivariate Gaussian Measures -- 2.1.3 Hermite Polynomials -- 2.2 Gaussian Measures on Separable Locally Convex Spaces -- 2.2.1 Cylindrical Sets -- 2.2.2 Definition and Basic Properties of Gaussian Measures -- 2.3 Cameron-Martin Space -- 2.4 Gaussian Product Measures -- 2.5 Gaussian Series -- 2.5.1 Some Abstract Results -- 2.5.2 Karhunen-Loève Expansion -- 2.5.3 Multiresolution Representations of GRFs -- 2.5.4 Periodic Continuation of a Stationary ; GRF -- 2.5.5 Sampling Stationary GRFs -- 2.6 Finite Element Discretization -- 2.6.1 Function Spaces -- 2.6.2 Finite Element Interpolation -- 3 Elliptic Divergence-Form PDEs with Log-Gaussian Coefficient -- 3.1 Statement of the Problem and Well-Posedness -- 3.2 Lipschitz Continuous Dependence -- 3.3 Regularity of the Solution -- 3.4 Random Input Data -- 3.5 Parametric Deterministic Coefficient -- 3.5.1 Deterministic Countably Parametric Elliptic PDEs -- 3.5.2 Probabilistic Setting -- 3.5.3 Deterministic Complex-Parametric Elliptic PDEs -- 3.6 Analyticity and Sparsity -- 3.6.1 Parametric Holomorphy -- 3.6.2 Sparsity of Wiener-Hermite PC Expansion Coefficients -- 3.7 Parametric Hs(D)-Analyticity and Sparsity -- 3.7.1 Hs(D)-Analyticity -- 3.7.2 Sparsity of Wiener-Hermite PC Expansion Coefficients -- 3.8 Parametric Kondrat'ev Analyticity and Sparsity -- 3.8.1 Parametric Ks(D)-Analyticity -- 3.8.2 Sparsity of Ks-Norms of Wiener-Hermite PC Expansion Coefficients -- 3.9 Bibliographical Remarks -- 4 Sparsity for Holomorphic Functions.; 4.1 (b,ξ,δ,X)-Holomorphy and Sparsity -- 4.2 (b,ξ,δ,X)-Holomorphy of Composite Functions -- 4.3 Examples of Holomorphic Data-to-Solution Maps -- 4.3.1 Linear Elliptic Divergence-Form PDE with Parametric Diffusion Coefficient -- 4.3.2 Linear Parabolic PDE with Parametric Coefficient -- 4.3.3 Linear Elastostatics with Log-Gaussian Modulus of Elasticity -- 4.3.4 Maxwell Equations with Log-Gaussian Permittivity -- 4.3.5 Linear Parametric Elliptic Systems and Transmission Problems -- 5 Parametric Posterior Analyticity and Sparsity in BIPs -- 5.1 Formulation and Well-Posedness -- 5.2 Posterior Parametric Holomorphy -- 5.3 Example: Parametric Diffusion Coefficient -- 6 Smolyak Sparse-Grid Interpolation and Quadrature -- 6.1 Smolyak Sparse-Grid Interpolation and Quadrature -- 6.1.1 Smolyak Sparse-Grid Interpolation -- 6.1.2 Smolyak Sparse-Grid Quadrature -- 6.2 Multiindex Sets -- 6.2.1 Number of Function Evaluations -- 6.2.2 Construction of (ck,ν)νF -- 6.2.3 Summability Properties of the Collection (ck,ν)νF -- 6.2.4 Computing -- 6.3 Interpolation Convergence Rate -- 6.4 Quadrature Convergence Rate -- 7 Multilevel Smolyak Sparse-Grid Interpolation and Quadrature -- 7.1 Setting and Notation -- 7.2 Multilevel Smolyak Sparse-Grid Algorithms -- 7.3 Construction of an Allocation of Discretization Levels -- 7.4 Multilevel Smolyak Sparse-Grid Interpolation Algorithm -- 7.5 Multilevel Smolyak Sparse-Grid Quadrature Algorithm -- 7.6 Examples for Multilevel Interpolation and Quadrature -- 7.6.1 Parametric Diffusion Coefficient in Polygonal Domain -- 7.6.2 Parametric Holomorphy of the Posterior Density in Bayesian PDE Inversion -- 7.7 Linear Multilevel Interpolation and Quadrature Approximation -- 7.7.1 Multilevel Smolyak Sparse-Grid Interpolation -- 7.7.2 Multilevel Smolyak Sparse-Grid Quadrature -- 7.7.3 Applications to Parametric Divergence-Form EllipticPDEs.; 7.7.4 Applications to Holomorphic Functions -- 8 Conclusions -- References -- Index.
• Sommario/riassunto: The present book develops the mathematical and numerical analysis of linear, elliptic and parabolic partial differential equations (PDEs) with coefficients whose logarithms are modelled as Gaussian random fields (GRFs), in polygonal and polyhedral physical domains. Both, forward and Bayesian inverse PDE problems subject to GRF priors are considered. Adopting a pathwise, affine-parametric representation of the GRFs, turns the random PDEs into equivalent, countably-parametric, deterministic PDEs, with nonuniform ellipticity constants. A detailed sparsity analysis of Wiener-Hermite polynomial chaos expansions of the corresponding parametric PDE solution families by analytic continuation into the complex domain is developed, in corner- ; and edge-weighted function spaces on the physical domain. The presented Algorithms and results are relevant for the mathematical analysis of many approximation methods for PDEs with GRF inputs, suchas model order reduction, neural network and tensor-formatted surrogates of parametric solution families. They are expected to impact computational uncertainty quantification subject to GRF models of uncertainty in PDEs, and are of interest for researchers and graduate students in both, applied and computational mathematics, as well as in computational science and engineering.