Probability for finance (Q2868663)

The book provides a concise but rigorous account of the probabilistic ideas and techniques most commonly used in the mathematical modeling of financial markets. The authors focus on the basic concepts of probability theory underlying widely used market models. In the first two chapters probability spaces, distributions and random variables are introduced from scratch. Principal aspects of measures and integrals including the construction of the Lebesgue integral and convergence theorems for integrals are presented. Chapter 3 introduces product measures, independency and random vectors, while Chapter 4 is devoted to a thorough discussion of conditioning. The final chapter explores key limit theorems for sequences of random variables, concluding with an introduction to weak convergence and the central limit theorem for independent identically distributed random variables. The book will be useful both for pure mathematicians who begin to study probability theory and for the specialists in finance and in other domains of applications of probabilistic concepts.