A Cookbook with Probability One

This book offers accessible probabilistic modelling of relevant financial problems. It is divided into two parts. The first part (cookbook) is written by emphasizing the key definitions and theorems without wasting too much of the reader with unnecessary technical details. Here, the first kind of target audience is graduate students in Economics with no prior exposition to probability theory (except for undergraduate courses in Applied Statistics) which are provided by a self-contained account of probabilistic modelling mainly applied to finance. The fundamental concepts of random variable/vector and probability distributions are introduced beforehand with respect to the usual treatment of this subject in standard probability textbook, trying to strike a balance between precise mathematical definitions and their applied knowledge. All the analytic tools developed are illustrated through examples of probability distributions of future stock prices, returns and profit and loss, together with their main characteristics, such as moments, moment generating and characteristic functions, location-scale families, and quantiles. The extension to the multivariate case for fixed time horizons is presented, together with the fundamentals of stochastic processes both in discrete and continuous time as candidate models for asset prices and return dynamics. Convergence concepts are presented as applied to the problem of point estimation of means, variances, correlation coefficients and risk measures. Short sections on risk and copula functions, further illustrate the potential application of probability models to financial problems. The second part of the book can be accessed by those students with more mathematical preparation. All the relevant proofs of results which are only stated in the first part and some advanced exercises with complete solutions are presented.

Supplements cookbook presentation of probability theory with the necessary mathematical rigor Yields a self-contained treatment of special applications such as risk measures Provides accessible probabilistic modelling of relevant financial problems

Auteur

Professor Damiano Rossello has a degree in Economics and a Ph.D. in Mathematics for Economics and Finance from the University of Catania. His research is focused on probabilistic and computational aspects of risk management as well as portfolio optimization. He is currently an associate professor at the University of Catania, where he has been teaching graduate courses in Probability for Finance and undergraduate courses in Mathematics of Finance.

Contenu

1 Probability, Events and Random Variables.- 2 Distribution of Random Variables.- 3 Multidimensional Random Variables.- 4 Moments and the Alike.- 5 Special Distributions.- 6 Conditioning.- 7 Regression, Prediction and more Dependence.- 8 Convergence Concepts.- 9 Introduction to Stochastic Processes.- 10 Introduction to Market Risk Measures.