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However, these models have been open to criticism as providing justification for discrimination against specific ethnic groups by law enforcement personnel. Whether this is statistically correct or a self-fulfilling correlation remains under debate. [8] Another example is the use of actuarial models to assess the risk of sex offense recidivism.
A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. The random variation is usually based on fluctuations observed in historical data for a selected period using standard time-series techniques.
In credibility theory, a branch of study in actuarial science, the Bühlmann model is a random effects model (or "variance components model" or hierarchical linear model) used to determine the appropriate premium for a group of insurance contracts. The model is named after Hans Bühlmann who first published a description in 1967. [1]
Wilkie, A. D. (1984) "A stochastic investment model for actuarial use", Transactions of the Faculty of Actuaries, 39: 341-403 Østergaard, Søren Duus (1971) "Stochastic Investment Models and Decision Criteria", The Swedish Journal of Economics, 73 (2), 157-183 JSTOR 3439055
Credibility theory is a branch of actuarial mathematics concerned with determining risk premiums. [1] To achieve this, it uses mathematical models in an effort to forecast the number of insurance claims based on past observations.
Actuaries began to forecast losses using models of random events instead of deterministic methods. Computers further revolutionized the actuarial profession. From pencil-and-paper to punchcards to microcomputers, the modeling and forecasting ability of the actuary has grown vastly. [46]
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.
De Moivre's Law is a survival model applied in actuarial science, named for Abraham de Moivre. [ 1 ] [ 2 ] [ 3 ] It is a simple law of mortality based on a linear survival function . Definition