An approach to actuarial modeling with Quasi-Monte Carlo: simulation of random sums depending on stochastic factors

The problem of estimating the characteristics of a random sum, when the number of summands is also random, is addressed. The considered case includes an additional stochastic factor: although the summed random variables come from a distribution of a known form, the parameters of this distribution are stochastic and can themselves be viewed as random variables (with known distributions). The Quasi-Monte-Carlo techniques are used to handle this problem and to analyze its efficiency relative to the regular Monte-Carlo simulation methods. The typical area of the application of the investigations is actuarial practice which often deals with random sums of financial losses. Besides actuarial applications, the proposed method may be useful in application to certain problems in informatics, related to the aggregation of heavy-tailed data.