scholarly journals Estimating Ruin Probability in an Insurance Risk Model with Stochastic Premium Income Based on the CFS Method

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 982
Author(s):  
Yujuan Huang ◽  
Jing Li ◽  
Hengyu Liu ◽  
Wenguang Yu
Keyword(s):  
Fourier Series ◽  
Ruin Probability ◽  
Risk Model ◽  
Expansion Method ◽  
Nonparametric Estimator ◽  
Insurance Risk ◽  
Numerical Examples ◽  
Complex Fourier Series ◽  
Premium Income ◽  
Insurance Risk Model

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.

scholarly journals Randomized Dividends in a Discrete Insurance Risk Model with Stochastic Premium Income

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wenguang Yu
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Insurance Risk ◽  
Ruin Time ◽  
Expected Discounted Penalty Function ◽  
Recursion Formulas ◽  
Compound Binomial ◽  
Discounted Penalty Function ◽  
Premium Income ◽  
Insurance Risk Model

The compound binomial insurance risk model is extended to the case where the premium income process, based on a binomial process, is no longer a constant premium rate of 1 per period and insurer pays a dividend of 1 with a probabilityq0when the surplus is greater than or equal to a nonnegative integerb. The recursion formulas for expected discounted penalty function are derived. As applications, we present the recursion formulas for the ruin probability, the probability function of the surplus prior to the ruin time, and the severity of ruin. Finally, numerical example is also given to illustrate the effect of the related parameters on the ruin probability.

scholarly journals Studies on a Double Poisson-Geometric Insurance Risk Model with Interference

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yujuan Huang ◽  
Wenguang Yu
Keyword(s):  
Ruin Probability ◽  
Laplace Transformation ◽  
Risk Model ◽  
Stopping Time ◽  
Adjustment Coefficient ◽  
Insurance Risk ◽  
Numerical Examples ◽  
Lundberg Inequality ◽  
First Time ◽  
Insurance Risk Model

This paper mainly studies a generalized double Poisson-Geometric insurance risk model. By martingale and stopping time approach, we obtain adjustment coefficient equation, the Lundberg inequality, and the formula for the ruin probability. Also the Laplace transformation of the time when the surplus reaches a given level for the first time is discussed, and the expectation and its variance are obtained. Finally, we give the numerical examples.

scholarly journals A Dependent Insurance Risk Model with Surrender and Investment under the Thinning Process

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Wenguang Yu ◽  
Yujuan Huang
Keyword(s):  
Interest Rates ◽  
Upper Bound ◽  
Ruin Probability ◽  
Risk Model ◽  
Arrival Process ◽  
Insurance Risk ◽  
Martingale Theory ◽  
Thinning Process ◽  
First Time ◽  
Insurance Risk Model

A dependent insurance risk model with surrender and investment under the thinning process is discussed, where the arrival of the policies follows a compound Poisson-Geometric process, and the occurrences of the claim and surrender happen as the p-thinning process and the q-thinning process of the arrival process, respectively. By the martingale theory, the properties of the surplus process, adjustment coefficient equation, the upper bound of ruin probability, and explicit expression of ruin probability are obtained. Moreover, we also get the Laplace transformation, the expectation, and the variance of the time when the surplus reaches a given level for the first time. Finally, various trends of the upper bound of ruin probability and the expectation and the variance of the time when the surplus reaches a given level for the first time are simulated analytically along with changing the investment size, investment interest rates, claim rate, and surrender rate.

A NOTE ON THE INSURANCE RISK PROBLEM

2003 ◽  
Vol 17 (2) ◽  
pp. 199-203 ◽  
Author(s):  
Sheldon M. Ross
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Computational Approach ◽  
Insurance Risk ◽  
Insurance Risk Model

We give a new characterization of the ruin probability of the classical insurance risk model and use it to obtain bounds on and a computational approach for evaluating this probability.

scholarly journals Estimating the Expected Discounted Penalty Function in a Compound Poisson Insurance Risk Model with Mixed Premium Income

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 305 ◽  
Author(s):  
Yunyun Wang ◽  
Wenguang Yu ◽  
Yujuan Huang ◽  
Xinliang Yu ◽  
Hongli Fan
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Insurance Risk ◽  
Compound Poisson ◽  
Expected Discounted Penalty Function ◽  
Fourier Cosine ◽  
Discounted Penalty Function ◽  
Premium Income ◽  
Expected Discounted Penalty ◽  
Insurance Risk Model

In this paper, we consider an insurance risk model with mixed premium income, in which both constant premium income and stochastic premium income are considered. We assume that the stochastic premium income process follows a compound Poisson process and the premium sizes are exponentially distributed. A new method for estimating the expected discounted penalty function by Fourier-cosine series expansion is proposed. We show that the estimation is easily computed, and it has a fast convergence rate. Some numerical examples are also provided to show the good properties of the estimation when the sample size is finite.

scholarly journals UPPER BOUNDS FOR RUIN PROBABILITY UNDER TIME SERIES MODELS

2006 ◽  
Vol 20 (3) ◽  
pp. 529-542 ◽  
Author(s):  
Gary K. C. Chan ◽  
Hailiang Yang
Keyword(s):  
Time Series ◽  
Ruin Probability ◽  
Causal Model ◽  
Risk Model ◽  
Upper Bounds ◽  
Time Series Models ◽  
Ruin Probabilities ◽  
Insurance Risk ◽  
Special Cases ◽  
Insurance Risk Model

In this article, we consider an insurance risk model where the claim and premium processes follow some time series models. We first consider the model proposed in Gerber [2,3]; then a model with dependent structure between premium and claim processes modeled by using Granger's causal model is considered. By using some martingale arguments, Lundberg-type upper bounds for the ruin probabilities under both models are obtained. Some special cases are discussed.

Affine Storage and Insurance Risk Models

2021 ◽  
Author(s):  
Onno Boxma ◽  
Michel Mandjes
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Affine Function ◽  
Insurance Risk ◽  
Risk Models ◽  
Special Cases ◽  
And Storage ◽  
Storage Processes ◽  
Do So ◽  
Insurance Risk Model

The aim of this paper is to analyze a general class of storage processes, in which the rate at which the storage level increases or decreases is assumed to be an affine function of the current storage level, and, in addition, both upward and downward jumps are allowed. To do so, we first focus on a related insurance risk model, for which we determine the ruin probability at an exponentially distributed epoch jointly with the corresponding undershoot and overshoot, given that the capital level at time 0 is exponentially distributed as well. The obtained results for this insurance risk model can be translated in terms of two types of storage models, in one of those two cases by exploiting a duality relation. Many well-studied models are shown to be special cases of our insurance risk and storage models. We conclude by showing how the exponentiality assumptions can be greatly relaxed.

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