Metody MC zdarzeń rzadkich i ich zastosowanie w teorii ubezpieczeń - Rolski, Tomasz (MC Methods of Rare Events and Their Application in Insurance, 2006)
The theory of rare events allows for computing probabilities of events which are very small. One considers a family {A(u),u > 0} such that limu→∞ P(A(u)) = 0 , and looks for ղ(u) such that P(A(u)) = Eղ(u), fulfilling the following optimality property limsupu→∞ Var(ղ(u))/(Eղ(u))2 < ∞. Such an estimator can be deviced by the method of importance sampling (IS) or conditioning. To illustrate we show two examples requiring two approaches: (a) simulations of solvency probability for a portfolio of life insurances and (b) simulation of ruin probabilities.
Prace Naukowe Akademii Ekonomicznej we Wrocławiu; 2006; nr 1108, s. 55-65