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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.
In the late 1980s and early 1990s, there was a distinct effort for actuaries to combine financial theory and stochastic methods into their established models. [12] Ideas from financial economics became increasingly influential in actuarial thinking, and actuarial science has started to embrace more sophisticated mathematical modelling of ...
Actuarial credibility describes an approach used by actuaries to improve statistical estimates. Although the approach can be formulated in either a frequentist or Bayesian statistical setting, the latter is often preferred because of the ease of recognizing more than one source of randomness through both "sampling" and "prior" information.
This page is concerned with the stochastic modelling as applied to the insurance industry. For other stochastic modelling applications, please see Monte Carlo method and Stochastic asset models. For mathematical definition, please see Stochastic process. "Stochastic" means being or having a random variable.
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.
The following outline is provided as an overview of and topical guide to actuarial science: Actuarial science – discipline that applies mathematical and statistical methods to assess risk in the insurance and finance industries.
The output of a cat model is an estimate of the losses that the model predicts would be associated with a particular event or set of events. When running a probabilistic model , the output is either a probabilistic loss distribution or a set of events that could be used to create a loss distribution; probable maximum losses ("PMLs") and average ...
In geostatistical models, sampled data are interpreted as the result of a random process. The fact that these models incorporate uncertainty in their conceptualization doesn't mean that the phenomenon – the forest, the aquifer, the mineral deposit – has resulted from a random process, but rather it allows one to build a methodological basis for the spatial inference of quantities in ...