scholarly journals A Weighted Estimation for Risk Model

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Mei Ling Huang ◽  
Ke Zhao
Keyword(s):  
Pareto Distribution ◽  
Risk Model ◽  
Estimation Method ◽  
Risk Models ◽  
Semiparametric Method ◽  
The Usa ◽  
Heavy Tailed ◽  
Truncated Pareto ◽  
Weighted Estimation ◽  
Infinite Moments

We propose a weighted estimation method for risk models. Two examples of natural disasters are studied: hurricane loss in the USA and forest fire loss in Canada. Risk data is often fitted by a heavy-tailed distribution, for example, a Pareto distribution, which has many applications in economics, actuarial science, survival analysis, networks, and other stochastic models. There is a difficulty in the inference of the Pareto distribution which has infinite moments in the heavy-tailed case. Firstly this paper applies the truncated Pareto distribution to overcome this difficulty. Secondly, we propose a weighted semiparametric method to estimate the truncated Pareto distribution. The idea of the new method is to place less weight on the extreme data values. This paper gives an exact efficiency function, L1-optimal weights and L2-optimal weights of the new estimator. Monte Carlo simulation results confirm the theoretical conclusions. The two above mentioned examples are analyzed by using the proposed method. This paper shows that the new estimation method is more efficient by mean square error relative to several existing methods and fits risk data well.

scholarly journals A Cluster Truncated Pareto Distribution and Its Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mei Ling Huang ◽  
Vincenzo Coia ◽  
Percy Brill
Keyword(s):  
Real World ◽  
Goodness Of Fit ◽  
Pareto Distribution ◽  
Estimation Method ◽  
Estimation Methods ◽  
Real World Data ◽  
Goodness Of Fit Tests ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed ◽  
Truncated Pareto

The Pareto distribution is a heavy-tailed distribution with many applications in the real world. The tail of the distribution is important, but the threshold of the distribution is difficult to determine in some situations. In this paper we consider two real-world examples with heavy-tailed observations, which leads us to propose a mixture truncated Pareto distribution (MTPD) and study its properties. We construct a cluster truncated Pareto distribution (CTPD) by using a two-point slope technique to estimate the MTPD from a random sample. We apply the MTPD and CTPD to the two examples and compare the proposed method with existing estimation methods. The results of log-log plots and goodness-of-fit tests show that the MTPD and the cluster estimation method produce very good fitting distributions with real-world data.

scholarly journals A simulation of the insurance industry: the problem of risk model homogeneity

2021 ◽  
Author(s):  
Torsten Heinrich ◽  
Juan Sabuco ◽  
J. Doyne Farmer
Keyword(s):  
Risk Model ◽  
Insurance Industry ◽  
Solvency Ii ◽  
Insurance Companies ◽  
Risk Models ◽  
Catastrophe Insurance ◽  
Balance Sheets ◽  
Cat Bonds ◽  
European Regulatory ◽  
Heavy Tailed

AbstractWe develop an agent-based simulation of the catastrophe insurance and reinsurance industry and use it to study the problem of risk model homogeneity. The model simulates the balance sheets of insurance firms, who collect premiums from clients in return for insuring them against intermittent, heavy-tailed risks. Firms manage their capital and pay dividends to their investors and use either reinsurance contracts or cat bonds to hedge their tail risk. The model generates plausible time series of profits and losses and recovers stylized facts, such as the insurance cycle and the emergence of asymmetric firm size distributions. We use the model to investigate the problem of risk model homogeneity. Under the European regulatory framework Solvency II, insurance companies are required to use only certified risk models. This has led to a situation in which only a few firms provide risk models, creating a systemic fragility to the errors in these models. We demonstrate that using too few models increases the risk of nonpayment and default while lowering profits for the industry as a whole. The presence of the reinsurance industry ameliorates the problem but does not remove it. Our results suggest that it would be valuable for regulators to incentivize model diversity. The framework we develop here provides a first step toward a simulation model of the insurance industry, which could be used to test policies and strategies for capital management.

The application of the Pareto distribution to approximate income distributions of wealthy households in Poland

2021 ◽  
Vol 66 (5) ◽  
pp. 43-59
Author(s):  
Dorota Pekasiewicz
Keyword(s):  
Pareto Distribution ◽  
Estimation Method ◽  
Similarity Measures ◽  
Likelihood Estimation ◽  
Equivalent Income ◽  
Income Distributions ◽  
Pareto Model ◽  
Heavy Tailed ◽  
High Level ◽  
Maximum Likelihood Estimation Method

The aim of the paper is to approximate the equivalent income distributions of wealthy households in particular socio-economic groups using the Pareto distribution, with parameters estimated by means of the maximum likelihood estimation method. Households whose income exceeded the established wealth threshold were classified as wealthy households. Income distributions of wealthy households are usually non-modal and heavy-tailed, thus, the Pareto distribution was applied as their theoretical model. The equivalent income of wealthy households in Poland was analysed in total and in particular socio-economic groups. The research was based on data from the 2014–2017 Household Budget Survey. Selected similarity measures were used to examine the degree to which the theoretical distributions proved consistent with the empirical ones. The obtained results confirmed the high level of consistency of empirical income distributions with the Pareto model. Moreover, very good approximations were obtained especially for wealthy households of employees and self-employed, as well as pensioners. Slightly worse results were obtained for the farmers group. Theoretical distributions well fitted to empirical data were used to estimate selected distribution characteristics, including measures of location, dispersion and inequality, and to compare the different groups in terms of their wealth.

scholarly journals A general stochastic model for bivariate episodes driven by a gamma sequence

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Charles K. Amponsah ◽  
Tomasz J. Kozubowski ◽  
Anna K. Panorska
Keyword(s):  
Stochastic Model ◽  
Joint Distribution ◽  
Pareto Distribution ◽  
Integral Transforms ◽  
Bivariate Distribution ◽  
Conditional Distributions ◽  
General Stochastic Model ◽  
Heavy Tailed ◽  
Discrete Pareto Distribution ◽  
Special Case

AbstractWe propose a new stochastic model describing the joint distribution of (X,N), where N is a counting variable while X is the sum of N independent gamma random variables. We present the main properties of this general model, which include marginal and conditional distributions, integral transforms, moments and parameter estimation. We also discuss in more detail a special case where N has a heavy tailed discrete Pareto distribution. An example from finance illustrates the modeling potential of this new mixed bivariate distribution.

scholarly journals A Method for Confidence Intervals of High Quantiles

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 70
Author(s):  
Mei Ling Huang ◽  
Xiang Raney-Yan
Keyword(s):  
Confidence Intervals ◽  
Computational Algorithm ◽  
Geometric Mean ◽  
Asymptotic Properties ◽  
Quantile Estimation ◽  
Heavy Tailed Distributions ◽  
High Quantiles ◽  
High Quantile ◽  
Heavy Tailed ◽  
Infinite Moments

The high quantile estimation of heavy tailed distributions has many important applications. There are theoretical difficulties in studying heavy tailed distributions since they often have infinite moments. There are also bias issues with the existing methods of confidence intervals (CIs) of high quantiles. This paper proposes a new estimator for high quantiles based on the geometric mean. The new estimator has good asymptotic properties as well as it provides a computational algorithm for estimating confidence intervals of high quantiles. The new estimator avoids difficulties, improves efficiency and reduces bias. Comparisons of efficiencies and biases of the new estimator relative to existing estimators are studied. The theoretical are confirmed through Monte Carlo simulations. Finally, the applications on two real-world examples are provided.

scholarly journals Ruin problems in Markov-modulated risk models

2017 ◽  
Vol 12 (1) ◽  
pp. 23-48 ◽  
Author(s):  
David C.M. Dickson ◽  
Marjan Qazvini
Keyword(s):  
Continuous Time ◽  
Risk Model ◽  
Numerical Algorithms ◽  
Binomial Model ◽  
Risk Models ◽  
Time Of Ruin ◽  
Compound Binomial ◽  
Compound Binomial Model ◽  
Markov Modulated ◽  
The Time Of Ruin

AbstractChen et al. (2014), studied a discrete semi-Markov risk model that covers existing risk models such as the compound binomial model and the compound Markov binomial model. We consider their model and build numerical algorithms that provide approximations to the probability of ultimate ruin and the probability and severity of ruin in a continuous time two-state Markov-modulated risk model. We then study the finite time ruin probability for a discrete m-state model and show how we can approximate the density of the time of ruin in a continuous time Markov-modulated model with more than two states.

scholarly journals On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment

1984 ◽  
Vol 14 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Jean-Marie Reinhard
Keyword(s):  
Risk Model ◽  
Risk Process ◽  
Ruin Probabilities ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Risk Models ◽  
Markovian Environment ◽  
Necessary And Sufficient ◽  
Natural Way ◽  
Quantities Of Interest

AbstractWe consider a risk model in which the claim inter-arrivals and amounts depend on a markovian environment process. Semi-Markov risk models are so introduced in a quite natural way. We derive some quantities of interest for the risk process and obtain a necessary and sufficient condition for the fairness of the risk (positive asymptotic non-ruin probabilities). These probabilities are explicitly calculated in a particular case (two possible states for the environment, exponential claim amounts distributions).

scholarly journals Heavy Tailed Pareto Distribution: Properties and Applications

2021 ◽  
Vol 18 (4) ◽  
pp. 828-845
Author(s):  
K. Jayakumar ◽  
A. P. Kuttykrishnan ◽  
Bindu Krishnan
Keyword(s):  
Pareto Distribution ◽  
Heavy Tailed
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