Encyclopedia of Financial Models III

Concepts of Probability Theory

MARKUS HÖCHSTÖTTER, PhD

Assistant Professor, University of Karlsruhe

SVETLOZAR T. RACHEV, PhD, Dr Sci

Frey Family Foundation Chair-Professor, Department of Applied Mathematics and Statistics, Stony Brook University, and Chief Scientist, FinAnalytica

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

Abstract: Probability theory is the mathematical approach to formalizing the uncertainty of events. Even though a decision maker may not know which one of the set of possible events may finally occur, with probability theory, a decision maker has the means of providing each event with a certain probability. Furthermore, it provides the decision maker with the axioms to compute the probability of a composed event in a unique way. The rather formal environment of probability theory translates in a reasonable manner to the problems related to risk and uncertainty in finance such as, for example, the future price of a financial asset. Today, investors may be aware of the price of a certain asset, but they cannot say for sure what value it might have tomorrow. To make a prudent decision, investors need to assess the possible scenarios for tomorrow's price and assign to each scenario a probability of occurrence. Only then can investors reasonably determine whether the financial asset will satisfy an investment objective.

Probability theory serves as the quantification of risk in finance. To estimate probabilistic models, we have ...