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.
Keywords:
elements;
uncountable;
equality;
empty set;
union operator;
intersection operator;
pairwise disjoint;
complement;
right-continuous function;
non-decreasing function;
space;
subsets;
events;
elementary events;
atoms;
power set;
closed under countable unions;
closed under countable intersections;
algebra;
Borel;
measurable space;
probability measure;
mutually exclusive;
countable additivity;
probability space;
P-almost surely (P-a.s.);
unlikely;
certain event with respect to P;
Definition 6—Distribution function;
distribution function of the probability measure P;
random variable;
stochastic;
measurable;
A-A′-measurable;
measurable;
random variable on a countable space;
random variable on the uncountable space;
probability law;
abscissa;
improbable event