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140122  eng 
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a 9780387215488

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1 

a Chung, Kai Lai

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0 
0 
a Elementary Probability Theory
h Elektronische Ressource
b With Stochastic Processes and an Introduction to Mathematical Finance
c by Kai Lai Chung, Farid AitSahlia

250 


a 4th ed. 2003

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a New York, NY
b Springer New York
c 2003, 2003

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a XIV, 404 p
b online resource

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a 1 Set  1.1 Sample sets  1.2 Operations with sets  1.3 Various relations  1.4 Indicator  Exercises  2 Probability  2.1 Examples of probability  2.2 Definition and illustrations  2.3 Deductions from the axioms  2.4 Independent events  2.5 Arithmetical density  Exercises  3 Counting  3.1 Fundamental rule  3.2 Diverse ways of sampling  3.3 Allocation models; binomial coefficients  3.4 How to solve it  Exercises  4 Random Variables  4.1 What is a random variable?  4.2 How do random variables come about?  4.3 Distribution and expectation  4.4 Integervalued random variables  4.5 Random variables with densities  4.6 General case  Exercises  Appendix 1: Borel Fields and General Random Variables  5 Conditioning and Independence  5.1 Examples of conditioning  5.2 Basic formulas  5.3 Sequential sampling  5.4 Pólya’s urn scheme  5.5 Independence and relevance  5.6 Genetical models  Exercises 

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a 6 Mean, Variance, and Transforms  6.1 Basic properties of expectation  6.2 The density case  6.3 Multiplication theorem; variance and covariance  6.4 Multinomial distribution  6.5 Generating function and the like  Exercises  7 Poisson and Normal Distributions  7.1 Models for Poisson distribution  7.2 Poisson process  7.3 From binomial to normal  7.4 Normal distribution  7.5 Central limit theorem  7.6 Law of large numbers  Exercises  Appendix 2: Stirling’s Formula and de MoivreLaplace’ Theorem  8 From Random Walks to Markov Chains  8.1 Problems of the wanderer or gambler  8.2 Limiting schemes  8.3 Transition probabilities  8.4 Basic structure of Markov chains  8.5 Further developments  8.6 Steady state  8.7 Winding up (or down?)  Exercises  Appendix 3: Martingale  9 MeanVariance Pricing Model  9.1 An investments primer  9.2 Asset return and risk  9.3 Portfolio allocation  9.4 Diversification 

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a 9.5 Meanvariance optimization  9.6 Asset return distributions  9.7 Stable probability distributions  Exercises  Appendix 4: Pareto and Stable Laws  10 Option Pricing Theory  10.1 Options basics  10.2 Arbitragefree pricing: 1period model  10.3 Arbitragefree pricing: Nperiod model  10.4 Fundamental asset pricing theorems  Exercises  General References  Answers to Problems  Values of the Standard Normal Distribution Function

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a Statistical Theory and Methods

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a Mathematics in Business, Economics and Finance

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a Statistics

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a Probability Theory

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a Social sciences / Mathematics

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a Probabilities

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a AitSahlia, Farid
e [author]

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7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

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a Undergraduate Texts in Mathematics

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a 10.1007/9780387215488

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u https://doi.org/10.1007/9780387215488?nosfx=y
x Verlag
3 Volltext

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a 519.2

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a In this edition two new chapters, 9 and 10, on mathematical finance are added. They are written by Dr. Farid AitSahlia, ancien eleve, who has taught such a course and worked on the research staff of several industrial and financial institutions. The new text begins with a meticulous account of the uncommon vocab ulary and syntax of the financial world; its manifold options and actions, with consequent expectations and variations, in the marketplace. These are then expounded in clear, precise mathematical terms and treated by the methods of probability developed in the earlier chapters. Numerous graded and motivated examples and exercises are supplied to illustrate the appli cability of the fundamental concepts and techniques to concrete financial problems. For the reader whose main interest is in finance, only a portion of the first eight chapters is a "prerequisite" for the study of the last two chapters. Further specific references may be scanned from the topics listed in the Index, then pursued in more detail
