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 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 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.

The Expected Discounted Penalty Function with Random Income under Stochastic Discount Interest Force

2010 ◽  
Vol 113-116 ◽  
pp. 378-381
Author(s):  
Wen Guang Yu ◽  
Zhi Liu
Keyword(s):  
Poisson Process ◽  
Penalty Function ◽  
Risk Model ◽  
Classical Model ◽  
Expected Discounted Penalty Function ◽  
Renewal Model ◽  
Interest Force ◽  
Discounted Penalty Function ◽  
Premium Income ◽  
Expected Discounted Penalty

We study the delayed risk model with random premium income. The premium process is not a linear function of time in contrast with the classical model, but a Poisson process which is also independent of the claim process. We shall consider the case where the discount interest process is no longer a constant in comparison with the classical expected discounted penalty function, but a stochastic interest driven by Poisson process and Wiener process. The expected discounted penalty function in the delayed renewal model is expressed in terms of the corresponding Gerber-Shiu function in the ordinary renewal model. The obtained results can be viewed as the discrete analogy of the classical Sparre-Anderson risk model.

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.

ON THE COMPOUND POISSON RISK MODEL WITH PERIODIC CAPITAL INJECTIONS

2017 ◽  
Vol 48 (1) ◽  
pp. 435-477 ◽  
Author(s):  
Zhimin Zhang ◽  
Eric C.K. Cheung ◽  
Hailiang Yang
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Random Variable ◽  
Claim Amount ◽  
Expected Discounted Penalty Function ◽  
Discounted Cost ◽  
Capital Injection ◽  
Discounted Penalty Function ◽  
S Model ◽  
Capital Injections

AbstractThe analysis of capital injection strategy in the literature of insurance risk models (e.g. Pafumi, 1998; Dickson and Waters, 2004) typically assumes that whenever the surplus becomes negative, the amount of shortfall is injected so that the company can continue its business forever. Recently, Nie et al. (2011) has proposed an alternative model in which capital is immediately injected to restore the surplus level to a positive level b when the surplus falls between zero and b, and the insurer is still subject to a positive ruin probability. Inspired by the idea of randomized observations in Albrecher et al. (2011b), in this paper, we further generalize Nie et al. (2011)'s model by assuming that capital injections are only allowed at a sequence of time points with inter-capital-injection times being Erlang distributed (so that deterministic time intervals can be approximated using the Erlangization technique in Asmussen et al. (2002)). When the claim amount is distributed as a combination of exponentials, explicit formulas for the Gerber–Shiu expected discounted penalty function (Gerber and Shiu, 1998) and the expected total discounted cost of capital injections before ruin are obtained. The derivations rely on a resolvent density associated with an Erlang random variable, which is shown to admit an explicit expression that is of independent interest as well. We shall provide numerical examples, including an application in pricing a perpetual reinsurance contract that makes the capital injections and demonstration of how to minimize the ruin probability via reinsurance. Minimization of the expected discounted capital injections plus a penalty applied at ruin with respect to the frequency of injections and the critical level b will also be illustrated numerically.

The mean chance of ultimate ruin time in random fuzzy insurance risk model

2017 ◽  
Vol 22 (12) ◽  
pp. 4123-4131 ◽  
Author(s):  
Sara Ghasemalipour ◽  
Behrouz Fathi-Vajargah
Keyword(s):  
Risk Model ◽  
Insurance Risk ◽  
Ruin Time ◽  
The Mean ◽  
Mean Chance ◽  
Insurance Risk Model

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.

Sign in / Sign up

Export Citation Format

Share Document