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1. |
Record Nr. |
UNINA9910574094003321 |
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Autore |
Song Iickho |
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Titolo |
Probability and Random Variables: Theory and Applications / / by Iickho Song, So Ryoung Park, Seokho Yoon |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 |
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ISBN |
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Edizione |
[1st ed. 2022.] |
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Descrizione fisica |
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1 online resource (506 pages) |
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Disciplina |
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Soggetti |
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Statistics |
Probabilities |
Statistical Theory and Methods |
Probability Theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Preface -- Chapter 1 - Preliminaries -- Chapter 2 - Fundamentals of Probability -- Chapter 3 - Random Variables -- Chapter 4 - Random Vectors -- Chapter 5 - Normal Random Vectors -- Chapter 6 - Convergence of Random Variables -- Answers to Selected Exercises -- Index. |
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Sommario/riassunto |
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This book discusses diverse concepts and notions – and their applications – concerning probability and random variables at the intermediate to advanced level. It explains basic concepts and results in a clearer and more complete manner than the extant literature. In addition to a range of concepts and notions concerning probability and random variables, the coverage includes a number of key advanced concepts in mathematics. Readers will also find unique results on e.g. the explicit general formula of joint moments and the expected values of nonlinear functions for normal random vectors. In addition, interesting applications of the step and impulse functions in discussions on random vectors are presented. Thanks to a wealth of examples and a total of 330 practice problems of varying difficulty, readers will have the opportunity to significantly expand their |
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knowledge and skills. The book is rounded out by an extensive index, allowing readers to quickly and easily find what they are looking for. Given its scope, the book will appeal to all readers with a basic grasp of probability and random variables who are looking to go one step further. It also offers a valuable reference guide for experienced scholars and professionals, helping them review and refine their expertise. |
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2. |
Record Nr. |
UNINA9910255041503321 |
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Autore |
Röman Jan R. M |
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Titolo |
Analytical Finance: Volume II : The Mathematics of Interest Rate Derivatives, Markets, Risk and Valuation / / by Jan R. M. Röman |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Palgrave Macmillan, , 2017 |
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ISBN |
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Edizione |
[1st ed. 2017.] |
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Descrizione fisica |
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1 online resource (XXXI, 728 p. 141 illus.) |
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Disciplina |
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Soggetti |
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Financial engineering |
Social sciences - Mathematics |
Capital market |
Financial risk management |
Financial Engineering |
Mathematics in Business, Economics and Finance |
Capital Markets |
Risk Management |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Pricing via Arbitrage -- The Central Limit Theorem -- The Binomial model -- More on Binomial models -- Finite difference methods -- Value-at-Risk - VaR -- Introduction to probability theory -- Stochastic integration -- Partial parabolic differential equations and Feynman-Kač -- The Black-Scholes-Merton model -- American versus European |
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options -- Analytical pricing formulas for American options -- Poisson processes and jump diffusion -- Diffusion models in general -- Hedging -- Exotic Options -- Volatility -- Something about weather derivatives -- A Practical guide to pricing -- Pricing using deflators -- Securities with dividends -- Some Fixed-Income securities and Black-Scholes. |
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Sommario/riassunto |
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Analytical Finance is a comprehensive introduction to the financial engineering of equity and interest rate instruments for financial markets. Developed from notes from the author's many years in quantitative risk management and modeling roles, and then for the Financial Engineering course at Malardalen University, it provides exhaustive coverage of vanilla and exotic mathematical finance applications for trading and risk management, combining rigorous theory with real market application. Volume I - Equity Derivatives Markets, Valuation and Risk Management. Coverage includes: The fundamentals of stochastic processes used in finance including the change of measure with Girsanov transformation and the fundamentals of probability throry. Discrete time models, such as various binomial models and numerical solutions to Partial Differential Equations (PDEs) Monte-Carlosimulations and Value-at-Risk (VaR) Continuous time models, such as Black-Scholes-Merton and similar with extensions Arbitrage theory in discrete and continuous time models Volume II - Interest Rate Derivative Markets, Valuation and Risk Management Coverage includes: Interest Rates including negative interest rates Valuation and model most kinds of IR instruments and their definitions. Bootstrapping; how to create an interest curve from prices of traded instruments. The multi curve framework and collateral discounting Difference of bootstrapping for trading and IR Risk Models and risk with positive and negative interest rates. Risk measures of IR instruments Option Adjusted Spread and embedded optionality. Pricing theory, calibration and stochastic processes of interest rates Numerical methods; Binomial and trinomial trees, PDEs (Crank-Nicholson), Newton-Raphson in 2 dimension. Black models, Normal models and Market models Pricing before and after the credit crises and the multiple curve framework. Valuation with collateral agreements, CVA, DVA and FVA. |
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