Abstract
This paper considers the estimation of ruin probability in an insurance risk model with stochastic premium income. We first show that the ruin probability can be approximated by the complex Fourier series (CFS) expansion method. Then, we construct a nonparametric estimator of the ruin probability and analyze its convergence. Numerical examples are also provided to show the efficiency of our method when the sample size is finite.
Highlights
In the classical insurance risk model, the premium rate is a constant and the premium collection is a linear function of time
This paper considers the following risk model that the premium income is no longer a linear function of time, but a stochastic process represented by a random sum, that is, Academic Editor: Eric Ulm
This paper introduces how to use the complex Fourier series (CFS) method to approximate the ruin probability under the stochastic premium income insurance risk model and gives a nonparametric estimation of the corresponding ruin probability
Summary
In the classical insurance risk model, the premium rate is a constant and the premium collection is a linear function of time. A large number of studies use statistical methods of parametric and nonparametric estimation to study the ruin probability, and the sample data information used in them, such as the number of claims, the scale of individual claims, etc., are obtained through observation in the actual operation of insurance companies This method gives the research certain feasibility and important practical significance. In most calculations, the expansion of CFS can make the problem simple and the formula refined, and only need to convert it to real Fourier series at the end This paper applies this new method to the ruin field, and hopes that it can continue and enrich the research results in the field.
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