Insurance Claim Amount Research Articles

Insurance coverage in unstable region: Managing insurance claim risk amid Kashmir's political landscape

This study investigates the impact of prolonged political unrest on insurance claim amounts in Kashmir. It examines the behavior and coverage provided by insurance companies in high-risk areas, focusing on the hazards and perils associated with terrorism and political uncertainty. By analyzing historical data on political violence and terrorism in Kashmir, the study reveals significant patterns and relationships through descriptive statistics. The findings demonstrate that higher levels of political violence and terrorism lead to increased losses for insurers. Moreover, the study underscores the necessity of tailoring insurance coverage to the specific risks in unstable regions. It suggests employing time series analysis for more accurate pricing of insurance policies during periods of political instability. These insights offer practical implications for insurance companies, policymakers, and stakeholders, facilitating more effective risk assessment, pricing, and risk management strategies in volatile areas. In addition to outlining general customer requirements, the study discusses the measures and regulations needed for commercial insurers to provide economical services in such contexts. This comprehensive analysis enhances the understanding of the effects of abnormal situations like prolonged political unrest in Kashmir. Ultimately, the study proposes the integration of time series analysis into insurance pricing models to better navigate periods of political instability.

Forecasting Life Insurance Loss Reserves Using Time Series Analysis.

Purpose: To determine an accurate predictive model that captures trends and seasonality in life insurance claims. Methodology: Time Series Analysis is used to forecast Secondary data on life insurance claims. The researcher aims at using a non-actuarial and accurate predictive model that captures trends and seasonality in life insurance claims over time. The dataset, comprising monthly claim amounts from May 2018 to March 2024 obtained from an insurance company. Findings: Life insurance claims increases with time hence the insurance companies are to set up an appropriate reserve to cater for future occurrence. It is realized that ARIMA (2,1,1) is appropriate for modelling the life insurance claim amounts with a least Log Likelihood value of -766.99, AIC value of 1521.97, AICc value of 1522.6, and BIC value of 1530.91. An ACF plot and Ljung Box test on the residuals shows the residuals are free from autocorrelation and free from heteroscedasticity respectively and hence the model is a white noise and adequate for further analysis. The result of the twelve months forecast indicates an increase in the life insurance claims. Unique contribution to theory, practice and policy: Managers in the insurance companies should focus on risk management and reserve allocation of fund in order to meet short term and long term claims settlement.

Health insurance claim amount prediction using statistical methods

Health insurance claim amount prediction using statistical methods

Estimating Copula-Based Extension of Tail Value-at-Risk and Its Application in Insurance Claim

Dependent Tail Value-at-Risk, abbreviated as DTVaR, is a copula-based extension of Tail Value-at-Risk (TVaR). This risk measure is an expectation of a target loss once the loss and its associated loss are above their respective quantiles but bounded above by their respective larger quantiles. In this paper, we propose nonparametric estimators for DTVaR and establish their property of consistency. Moreover, we also propose the variability measure around this expected value truncated by the quantiles, called the Dependent Conditional Tail Variance (DCTV). We use this measure for constructing confidence intervals of the DTVaR. Both parametric and nonparametric approaches for DTVaR estimations are explored. Furthermore, we assess the performance of DTVaR estimations using a proposed backtest based on the DCTV. As for the numerical study, we take an application in the insurance claim amount.

Feller-Pareto and Related Distributions: Numerical Implementation and Actuarial Applications

Actuaries model insurance claim amounts using heavy tailed probability distributions. They routinely need to evaluate quantities related to these distributions such as quantiles in the far right tail, moments or limited moments. Furthermore, actuaries often resort to simulation to solve otherwise untractable risk evaluation problems. The paper discusses our implementation of support functions for the Feller-Pareto distribution for the R package actuar. The Feller-Pareto defines a large family of heavy tailed distributions encompassing the transformed beta family and many variants of the Pareto distribution.

Gamma Mixture Density Networks and their application to modelling insurance claim amounts

We discuss how mixtures of Gamma distributions with mixing probabilities, shape and rate parameters depending on features can be fitted with neural networks. We develop two versions of the EM algorithm for fitting so-called Gamma Mixture Density Networks, which we call the EM network boosting algorithm and the EM forward network algorithm, and we test their implementation together with the choices of hyperparameters. A simulation study shows that our algorithms perform very well on synthetic data sets. We further illustrate the application of the Gamma Mixture Density Network on a real data set of motor insurance claim amounts and conclude that Gamma Mixture Density Networks can improve the fit of the regression model and the predictions of the claim severities used for rate-making compared to classical actuarial techniques.

Predictive Modeling of Insurance Claims Using Machine Learning Approach for Different Types of Motor Vehicles

The main objective of this research paper is to build an appropriate mathematical model that helps in forecasting third party claim amount for different categories of vehicles based on the chosen characteristics of the data. In actuarial research, predicting the insurance claim amount for different vehicle categories is a challenging task, and minimal empirical research studies were done to forecast the claims. In the present study, the annual time series historical data were collected for a period of 34 years. We had built the machine learning predictive models to modeling the claim amount with different categories of vehicles effectively. In this context, we exhibited the feasibility of using a statistical machine learning approach such as Linear regression Model, the Exponential Smoothing Model, autoregressive integrated moving average (ARIMA), artificial neural network (ANN), and hybrid ARIMA-ANN models to predict the various categories of vehicles claim amount. The data were analyzed, compared, and the empirical analysis showed that Artificial Neural Network is a better predictive model among the other time series models based on performance evaluation metrics RMSE and MAPE with lesser variance. Therefore, the machine learning approach for forecasting third party claim amounts will help the Insurance Companies in India to provide a better predictive model, which ensures better claims settlement and management for different categories of vehicles.

Better Housing: FHA Property Improvement Loans

The National Housing Act of 1934 is most well-known for creating the Federal Housing Administration (FHA) to insure home mortgages; however, the first section of the Act also covers insurance of financial institutions against losses on loans and advances of credit “for the purpose of financing alterations, repairs, and improvements upon real property.” Title I was at the heart of a New Deal initiative to modernize housing as both a means to improve the welfare of American households as well as employ surplus labor in home construction and repair. It also introduced commercial banks to consumer instalment lending, which revolutionized household finance. FHA endorsed more property improvement loans per year than home mortgages for its first 35 years. And the cumulative number of loans insured under Title I was greater than the more famous Section 203B program until the financial crisis of 2008. Yet the importance of Title I is often overlooked. “Historical scholars have argued that FHA programs were self-validating: by encouraging the neglect of older homes and neighborhoods, they made filtering inevitable, and with it the decline of older neighborhoods in central cities. There is some truth to this assessment of federal policy. However, and although the fact has been widely ignored, from the beginning the FHA also sought to improve existing homes and neighborhoods” (Harris 2009, p. 392). In part, this may be because the Title I program has not kept pace with changes in the financial industry, causing disbursements to tumble and the program to drift into obscurity. This paper briefly describes FHA’s Title I property improvement program, including its history and underwriting requirements. Using administrative data, the paper examines variation in interest rates across loan and borrower characteristics. In particular, I estimate the rate premium associated with unsecured lending during the Great Recession. I further estimate the likelihood of default and insurance claim amount given default. The results could be used to automate credit underwriting and facilitate modernization of property improvement financing.

Modeling and Predicting of Motor Insurance Claim Amount using Artificial Neural Network

In India the insurance industry is in its growth stage. It consists of 58 insurance companies of which 24 in life and 34 are non-life insurance. The Non-life Insurance companies which cater to motor insurance business presently utilize different trend models to forecast paid claim amount. Motor Insurance Claim amount prediction is one of the most difficult tasks to accomplish in financial forecasting due to the complex nature of data points. The main objective of this study is to determine a reliable time series forecasting model to predict own damage (OD) claim amount of motor insurance data in India from 1981 to 2016. In this context, the annual time series claim data was collected and modeled by using the Generalized linear model (GLM), Autoregressive Integrated Moving Average (ARIMA) and Artificial Neural Network (ANN) method. The validation of the model has been done by comparison of predicted and actual values for the period of 36 years. Also, different types of possible models were evaluated using Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), Mean Absolute Percentage Error (MAPE), and Root Mean Square Error (RMSE) for accuracy. The results showed that ANN outperformed other traditional time series models (GLM & ARIMA) for predicting the future own damage claim amount with a lesser residual error. Further, the outcome of these data analytics studies would help Insurance companies to have an idea about the expected future claim amounts with more accuracy. Thus, predicting the Motor insurance's own damage claim will help insurance companies to budget their future revenue.

Fitting Gamma Mixture Density Networks with Expectation-Maximization Algorithm

We discuss how mixtures of Gamma distributions with mixing probabilities, shape and rate parameters depending on features can be fitted with neural networks. We develop two versions of the EM algorithm for fitting so-called Gamma Mixture Density Networks, which we call the EM network boosting algorithm and the EM forward network algorithm, and we test their implementation together with the choices of hyperparameters. A simulation study shows that our algorithms perform very well on synthetic data sets. We further illustrate the application of the Gamma Mixture Density Network on a real data set of motor insurance claim amounts and conclude that Gamma Mixture Density Networks can improve the fit of the regression model and the predictions of the claim severities used for rate-making compared to classical actuarial techniques.

An EM Algorithm for Double-Pareto-Lognormal Generalized Linear Model Applied to Heavy-Tailed Insurance Claims

Generalized linear models might not be appropriate when the probability of extreme events is higher than that implied by the normal distribution. Extending the method for estimating the parameters of a double Pareto lognormal distribution (DPLN) in Reed and Jorgensen (2004), we develop an EM algorithm for the heavy-tailed Double-Pareto-lognormal generalized linear model. The DPLN distribution is obtained as a mixture of a lognormal distribution with a double Pareto distribution. In this paper the associated generalized linear model has the location parameter equal to a linear predictor which is used to model insurance claim amounts for various data sets. The performance is compared with those of the generalized beta (of the second kind) and lognorma distributions.

Fat-Tailed Regression with the DPLN Distribution

Traditional regression models might not be appropriate when the probability of extreme events is higher than that implied by the normal distribution. Extending the method for estimating the parameters of a double Pareto lognormal distribution (DPLN) in Reed and Jorgensen (2004), we develop an EM algorithm for heavy-tailed DPLN-regression. The DPLN distribution is obtained as a mixture of a lognormal distribution with a double Pareto distribution. In this paper the associated regression model has the location parameter equal to a linear predictor which is used to model insurance claim amounts for various data sets. The performance is compared with those of the generalised beta (of the second kind) and lognormal distributions.

Ruin probabilities and optimal investment when the stock price follows an exponential Lévy process

This paper investigates the infinite and finite time ruin probability under the condition that the company is allowed to invest a certain amount of money in some stock market, and the remaining reserve in the bond with constant interest force. The total insurance claim amount is modeled by a compound Poisson process and the price of the risky asset follows a general exponential Lévy process. Exponential type upper bounds for the ultimate ruin probability are derived when the investment is a fixed constant, which can be calculated explicitly. This constant investment strategy yields the optimal asymptotic decay of the ruin probability under some mild assumptions. Finally, we provide an approximation of the optimal investment strategy, which maximizes the expected wealth of the insurance company under a risk constraint on the Value-at-Risk.

On the infinite-horizon probability of (non)ruin for integer-valued claims

We consider a compound Poisson process whose jumps are modelled as a sequence of positive, integer-valued, dependent random variables, W1,W2,…, viewed as insurance claim amounts. The number of points up to time t of the stationary Poisson process which models the claim arrivals is assumed to be independent of W1,W2,…. The premium income to the insurance company is represented by a nondecreasing, nonnegative, real-valued function h(t) on [0,∞) such that limt→∞h(t) = ∞. The function h(t) is interpreted as an upper boundary. The probability that the trajectory of such a compound Poisson process will not cross the upper boundary in infinite time is known as the infinite-horizon nonruin probability. Our main result in this paper is an explicit expression for the probability of infinite-horizon nonruin, assuming that certain conditions on the premium-income function, h(t), and the joint distribution of the claim amount random variables, W1,W2,…, hold. We have also considered the classical ruin probability model, in which W1,W2,… are assumed to be independent, identically distributed random variables and we let h(t)=u + ct. For this model we give a formula for the nonruin probability which is a special case of our main result. This formula is shown to coincide with the infinite-horizon nonruin probability formulae of Picard and Lefèvre (2001), Gerber (1988), (1989), and Shiu (1987), (1989).

On the infinite-horizon probability of (non)ruin for integer-valued claims

We consider a compound Poisson process whose jumps are modelled as a sequence of positive, integer-valued, dependent random variables, W 1,W 2,…, viewed as insurance claim amounts. The number of points up to time t of the stationary Poisson process which models the claim arrivals is assumed to be independent of W 1,W 2,…. The premium income to the insurance company is represented by a nondecreasing, nonnegative, real-valued function h(t) on [0,∞) such that lim t→∞ h(t) = ∞. The function h(t) is interpreted as an upper boundary. The probability that the trajectory of such a compound Poisson process will not cross the upper boundary in infinite time is known as the infinite-horizon nonruin probability. Our main result in this paper is an explicit expression for the probability of infinite-horizon nonruin, assuming that certain conditions on the premium-income function, h(t), and the joint distribution of the claim amount random variables, W 1,W 2,…, hold. We have also considered the classical ruin probability model, in which W 1,W 2,… are assumed to be independent, identically distributed random variables and we let h(t)=u + ct. For this model we give a formula for the nonruin probability which is a special case of our main result. This formula is shown to coincide with the infinite-horizon nonruin probability formulae of Picard and Lefèvre (2001), Gerber (1988), (1989), and Shiu (1987), (1989).

Optimal investment for insurers

We consider a stochastic model for the wealth of an insurance company which has the possibility to invest into a risky and a riskless asset under a constant mix strategy. The total insurance claim amount is modeled by a compound Poisson process and the price of the risky asset follows a geometric Brownian motion. We investigate the resulting integrated risk process and the corresponding discounted net loss process. This opens up a way to measure the risk of a negative outcome of the integrated risk process in a stationary way. We provide an approximation of the optimal investment strategy, which maximizes the expected wealth under a risk constraint on the Value-at-Risk.