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Essential mathematics for market risk management [[electronic resource] /] / Simon Hubbert
Essential mathematics for market risk management [[electronic resource] /] / Simon Hubbert
Autore Hubbert Simon
Edizione [2nd ed.]
Pubbl/distr/stampa Hoboken, N.J., : Wiley, 2012
Descrizione fisica 1 online resource (354 p.)
Disciplina 658.15/50151
Collana Wiley finance
Soggetto topico Risk management - Mathematical models
Capital market - Mathematical models
ISBN 1-283-40482-6
9786613404824
1-118-37236-0
1-118-46721-3
1-119-95301-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Essential Mathematics for Market Risk Management; Contents; Preface; 1 Introduction; 1.1 Basic Challenges in Risk Management; 1.2 Value at Risk; 1.3 Further Challenges in Risk Management; 2 Applied Linear Algebra for Risk Managers; 2.1 Vectors and Matrices; 2.2 Matrix Algebra in Practice; 2.3 Eigenvectors and Eigenvalues; 2.4 Positive Definite Matrices; 3 Probability Theory for Risk Managers; 3.1 Univariate Theory; 3.1.1 Random variables; 3.1.2 Expectation; 3.1.3 Variance; 3.2 Multivariate Theory; 3.2.1 The joint distribution function; 3.2.2 The joint and marginal density functions
3.2.3 The notion of independence 3.2.4 The notion of conditional dependence; 3.2.5 Covariance and correlation; 3.2.6 The mean vector and covariance matrix; 3.2.7 Linear combinations of random variables; 3.3 The Normal Distribution; 4 Optimization Tools; 4.1 Background Calculus; 4.1.1 Single-variable functions; 4.1.2 Multivariable functions; 4.2 Optimizing Functions; 4.2.1 Unconstrained quadratic functions; 4.2.2 Constrained quadratic functions; 4.3 Over-determined Linear Systems; 4.4 Linear Regression; 5 Portfolio Theory I; 5.1 Measuring Returns
5.1.1 A comparison of the standard and log returns 5.2 Setting Up the Optimal Portfolio Problem; 5.3 Solving the Optimal Portfolio Problem; 6 Portfolio Theory II; 6.1 The Two-Fund Investment Service; 6.2 A Mathematical Investigation of the Optimal Frontier; 6.2.1 The minimum variance portfolio; 6.2.2 Covariance of frontier portfolios; 6.2.3 Correlation with the minimum variance portfolio; 6.2.4 The zero-covariance portfolio; 6.3 A Geometrical Investigation of the Optimal Frontier; 6.3.1 Equation of a tangent to an efficient portfolio; 6.3.2 Locating the zero-covariance portfolio
6.4 A Further Investigation of Covariance 6.5 The Optimal Portfolio Problem Revisited; 7 The Capital Asset Pricing Model (CAPM); 7.1 Connecting the Portfolio Frontiers; 7.2 The Tangent Portfolio; 7.2.1 The market's supply of risky assets; 7.3 The CAPM; 7.4 Applications of CAPM; 7.4.1 Decomposing risk; 8 Risk Factor Modelling; 8.1 General Factor Modelling; 8.2 Theoretical Properties of the Factor Model; 8.3 Models Based on Principal Component Analysis (PCA); 8.3.1 PCA in two dimensions; 8.3.2 PCA in higher dimensions; 9 The Value at Risk Concept; 9.1 A Framework for Value at Risk
9.1.1 A motivating example 9.1.2 Defining value at risk; 9.2 Investigating Value at Risk; 9.2.1 The suitability of value at risk to capital allocation; 9.3 Tail Value at Risk; 9.4 Spectral Risk Measures; 10 Value at Risk under a Normal Distribution; 10.1 Calculation of Value at Risk; 10.2 Calculation of Marginal Value at Risk; 10.3 Calculation of Tail Value at Risk; 10.4 Sub-additivity of Normal Value at Risk; 11 Advanced Probability Theory for Risk Managers; 11.1 Moments of a Random Variable; 11.2 The Characteristic Function; 11.2.1 Dealing with the sum of several random variables
11.2.2 Dealing with a scaling of a random variable
Record Nr. UNINA-9910141227803321
Hubbert Simon  
Hoboken, N.J., : Wiley, 2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Spherical Radial Basis Functions, Theory and Applications [[electronic resource] /] / by Simon Hubbert, Quôc Thông Le Gia, Tanya M. Morton
Spherical Radial Basis Functions, Theory and Applications [[electronic resource] /] / by Simon Hubbert, Quôc Thông Le Gia, Tanya M. Morton
Autore Hubbert Simon
Edizione [1st ed. 2015.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Descrizione fisica 1 online resource (150 p.)
Disciplina 515.53
Collana SpringerBriefs in Mathematics
Soggetto topico Approximation theory
Partial differential equations
Numerical analysis
Global analysis (Mathematics)
Manifolds (Mathematics)
Geophysics
Approximations and Expansions
Partial Differential Equations
Numerical Analysis
Global Analysis and Analysis on Manifolds
Geophysics/Geodesy
ISBN 3-319-17939-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Motivation and Background Functional Analysis -- The Spherical Basis Function Method -- Error Bounds via Duchon's Technique -- Radial Basis Functions for the Sphere -- Fast Iterative Solvers for PDEs on Spheres -- Parabolic PDEs on Spheres.
Record Nr. UNINA-9910299768503321
Hubbert Simon  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui