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In actuarial science and applied probability, ruin theory (sometimes risk theory [1] or collective risk theory) uses mathematical models to describe an insurer's vulnerability to insolvency/ruin. In such models key quantities of interest are the probability of ruin, distribution of surplus immediately prior to ruin and deficit at time of ruin.
Risk is the lack of certainty about the outcome of making a particular choice. Statistically, the level of downside risk can be calculated as the product of the probability that harm occurs (e.g., that an accident happens) multiplied by the severity of that harm (i.e., the average amount of harm or more conservatively the maximum credible amount of harm).
where is the value function (typical form shown in Figure 1), is the weighting function (as sketched in Figure 2) and ():=, i.e. the integral of the probability measure over all values up to , is the cumulative probability. This generalizes the original formulation by Tversky and Kahneman from finitely many distinct outcomes to infinite (i.e ...
A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics—particularly Bayesian statistics—and machine learning.
The theory of subjective expected utility combines two concepts: first, a personal utility function, and second, a personal probability distribution (usually based on Bayesian probability theory). This theoretical model has been known for its clear and elegant structure and its considered by some researchers to be "the most brilliant axiomatic ...
Sometimes the same risk will be assigned to different tasks. In this case the name of risk will be the same for different arrows pointing to different bars. Risk probability and impact can be written next to the arrow. It is possible to cut names “Probability:” to “Prob:”, or just “P:”, and “Impact:” to “Imp:”, or just “I:”.
An example p-box is shown in the figure at right for an uncertain number x consisting of a left (upper) bound and a right (lower) bound on the probability distribution for x. The bounds are coincident for values of x below 0 and above 24. The bounds may have almost any shape, including step functions, so long as they are monotonically ...
Risk premium is the product of the market price of risk and the quantity of risk, and the risk is the standard deviation of the portfolio. The CML equation is : R P = I RF + (R M – I RF)σ P /σ M. where, R P = expected return of portfolio I RF = risk-free rate of interest R M = return on the market portfolio σ M = standard deviation of the ...