scholarly journals The Asymptotics of Recovery Probability in the Dual Renewal Risk Model with Constant Interest and Debit Force

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Hao Wang ◽  
Lin Xu
Keyword(s):  
Asymptotic Behavior ◽  
Discrete Time ◽  
Risk Model ◽  
Continuous Time Model ◽  
Time Model ◽  
Discrete Time Model ◽  
Renewal Risk Model ◽  
Renewal Risk ◽  
Premium Income ◽  
Constant Interest

The asymptotic behavior of the recovery probability for the dual renewal risk model with constant interest and debit force is studied. By means the idea of Markov Skeleton method, we studied the times that the random premium incomes happened and transformed the continuous time model into a discrete time model. By investigating the fluctuations of this discrete time model, we obtained the asymptotic behavior when the random premium income belongs to a kind of heavy-tailed distributions.

Precise Large Deviation of Claim Surplus Process in a Renewal Risk Model with Random Premium Income

2013 ◽  
Vol 850-851 ◽  
pp. 771-775
Author(s):  
Ying Hua Dong
Keyword(s):  
Risk Model ◽  
Large Deviation ◽  
Compound Poisson Process ◽  
Dependence Structure ◽  
Arrival Times ◽  
Renewal Risk Model ◽  
Surplus Process ◽  
Precise Large Deviation ◽  
Renewal Risk ◽  
Premium Income

In this paper, we consider a nonstandard renewal risk model in which claim sizes and corresponding inter-arrival times form a sequence of independent and identically distributed random pairs. Each pair satisfies a certain dependence structure. In addition, premium income is described by a compound Poisson process. When the distribution of claim sizes belongs to the consistent variation class, we obtain precise large deviation of claim surplus process.

scholarly journals Solution of Ruin Probability for Continuous Time Model Based on Block Trigonometric Exponential Neural Network

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 876
Author(s):  
Yinghao Chen ◽  
Chun Yi ◽  
Xiaoliang Xie ◽  
Muzhou Hou ◽  
Yangjin Cheng
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Ruin Probability ◽  
Risk Model ◽  
Insurance Company ◽  
Classical Risk Model ◽  
Continuous Time Model ◽  
Time Model ◽  
Trial Solution ◽  
Premium Income

The ruin probability is used to determine the overall operating risk of an insurance company. Modeling risks through the characteristics of the historical data of an insurance business, such as premium income, dividends and reinvestments, can usually produce an integral differential equation that is satisfied by the ruin probability. However, the distribution function of the claim inter-arrival times is more complicated, which makes it difficult to find an analytical solution of the ruin probability. Therefore, based on the principles of artificial intelligence and machine learning, we propose a novel numerical method for solving the ruin probability equation. The initial asset u is used as the input vector and the ruin probability as the only output. A trigonometric exponential function is proposed as the projection mapping in the hidden layer, then a block trigonometric exponential neural network (BTENN) model with a symmetrical structure is established. Trial solution is set to meet the initial value condition, simultaneously, connection weights are optimized by solving a linear system using the extreme learning machine (ELM) algorithm. Three numerical experiments were carried out by Python. The results show that the BTENN model can obtain the approximate solution of the ruin probability under the classical risk model and the Erlang(2) risk model at any time point. Comparing with existing methods such as Legendre neural networks (LNN) and trigonometric neural networks (TNN), the proposed BTENN model has a higher stability and lower deviation, which proves that it is feasible and superior to use a BTENN model to estimate the ruin probability.

DISCRETE AND CONTINUOUS TIME POPULATION MODELS, A COMPARISON CONCERNING PROLIFERATION BY FISSION

1995 ◽  
Vol 03 (02) ◽  
pp. 543-558 ◽  
Author(s):  
B.W. KOOI ◽  
M.P. BOER
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Matrix Theory ◽  
Dimensional Torus ◽  
Continuous Time Model ◽  
Time Model ◽  
Discrete Time Model ◽  
Fixed Part ◽  
Number Of Individuals ◽  
Insight Into

We present two approaches, discrete time and continuous time models, for individuals which propagate through binary fission. The volumes of the two daughters are a fixed part of that of the mother, not necessarily the half, and their growth rates may differ. The discrete time approach gives more insight into the results obtained with the continuous time model. We define classes in the continuous time model such that the total number of individuals in these classes at specific moments in time is equal to the unknown number in a discrete time model. Then the discrete time model is homologous to the continuous one in the sense of having the same solutions at specific moments. Population matrix theory applies when the ratio of the inter-division times of the two daughters is rational. There is inter-class convergence but no intra-class convergence. The latter feature implies that there is no convergence of the size distribution in the continuous time model either. When the ratio is irrational the continuous time model holds and there is convergence but the rate of convergence can become infinitesimally small. This phenomenon is linked with quasi-periodicity on a 2-dimensional torus.

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