Conditional probabilityIn probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(AB) or occasionally P_B(A).
Conditional probability distributionIn probability theory and statistics, given two jointly distributed random variables and , the conditional probability distribution of given is the probability distribution of when is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value of as a parameter. When both and are categorical variables, a conditional probability table is typically used to represent the conditional probability.
Conditional probability tableIn statistics, the conditional probability table (CPT) is defined for a set of discrete and mutually dependent random variables to display conditional probabilities of a single variable with respect to the others (i.e., the probability of each possible value of one variable if we know the values taken on by the other variables). For example, assume there are three random variables where each has states.
Conditional independenceIn probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of a hypothesis. Conditional independence is usually formulated in terms of conditional probability, as a special case where the probability of the hypothesis given the uninformative observation is equal to the probability without. If is the hypothesis, and and are observations, conditional independence can be stated as an equality: where is the probability of given both and .
Real options valuationReal options valuation, also often termed real options analysis, (ROV or ROA) applies option valuation techniques to capital budgeting decisions. A real option itself, is the right—but not the obligation—to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project. For example, real options valuation could examine the opportunity to invest in the expansion of a firm's factory and the alternative option to sell the factory.
Joint probability distributionGiven two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered for any given number of random variables. The joint distribution encodes the marginal distributions, i.e. the distributions of each of the individual random variables. It also encodes the conditional probability distributions, which deal with how the outputs of one random variable are distributed when given information on the outputs of the other random variable(s).
Conditional expectationIn probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value – the value it would take "on average" over an arbitrarily large number of occurrences – given that a certain set of "conditions" is known to occur. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of those values.
Regular conditional probabilityIn probability theory, regular conditional probability is a concept that formalizes the notion of conditioning on the outcome of a random variable. The resulting conditional probability distribution is a parametrized family of probability measures called a Markov kernel. Consider two random variables . The conditional probability distribution of Y given X is a two variable function If the random variable X is discrete If the random variables X, Y are continuous with density .
Contingent claimIn finance, a contingent claim is a derivative whose future payoff depends on the value of another “underlying” asset, or more generally, that is dependent on the realization of some uncertain future event. These are so named, since there is only a payoff under certain contingencies. Any derivative instrument that is not a contingent claim is called a forward commitment. The prototypical contingent claim is an option, the right to buy or sell the underlying asset at a specified exercise price by a certain expiration date; whereas (vanilla) swaps, forwards, and futures are forward commitments, since these grant no such optionality.
Corporate financeCorporate finance is the area of finance that deals with the sources of funding, and the capital structure of corporations, the actions that managers take to increase the value of the firm to the shareholders, and the tools and analysis used to allocate financial resources. The primary goal of corporate finance is to maximize or increase shareholder value. Correspondingly, corporate finance comprises two main sub-disciplines.
