Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathematical Finance
Springer Science & Business Media, Jul 14, 2006 - Mathematics - 404 pages
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.
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Elementary Probability Theory: With Stochastic Processes and an Introduction ...
K. L. Chung,Farid AitSahlia
No preview available - 2010
Algebra apply arbitrary argument asset assume Axiom ball drawn binomial binomial coefficients black balls calculus called cards central limit theorem Chapter coin compute conditional probability consider constant converges corresponding countable defined definition density function dice discussed disjoint distribution function equal equation event Example Exercise expected number finite follows formula given Hence Hint independent random variables infinite integers large numbers law of large Markov chain Markov property martingale mathematical means moment-generating function namely nonnegative normal distribution notation observe obtain one-period option outcomes pair particle Poisson distribution Poisson process portfolio positive possible probability distribution probability measure probability theory problem proof Proposition random walk recurrent replaced result riskless sample point sample space sequence stochastic subset Suppose tokens tossed total number transition matrix variance zero