Department of Statistics

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Modeling Large Insurance Claims Using Extreme Value Theory: A Case Study Of The 37 Military Hospital.
(University Of Ghana, 2020) Collins, A.
The private health insurance industry is one of the vital components in nation-building. It complements government’s efforts in reducing “out-of-pocket” payment for healthcare services in the country. However, some private health insurance companies face severe insolvency issues due to accumulation of unanticipated huge claim amounts. The Extreme Value Theory (EVT) is a statistical tool proven to help solve or mitigate some of these challenges since it focuses mainly on the behaviour of severe but rare occurrence. In this study, we employ the EVT approaches to model large insurance claims from the 37 Military hospital; and to estimate financial risk indicators such as Value-at-Risk (VaR) and Expected Shortfall (ES) among other extreme quantiles. Conclusions drawn from analysis established that the Weibull class of distributions is more appropriate for the data at hand and for this reason, it is not likely for the 37 Military hospital to submit claim amount exceeding 24,618 cedis for any given day. In addition, private health insurance firms can be assured at a confidence level of 99%, 99.5% and 99.9% that within a day, the hospital is not likely to submit a claim amount exceeding 2,910 cedis, 3,938 cedis and 7,946 cedis respectively. Finally, it was recommended that the NHIA could replicate this study using the claims received by the public health insurance scheme (i.e. NHIS) since it can go a long way to strengthen the financial sustainability of the scheme.
Survival Analysis Among Tuberculosis Patients: A Case Study of Adults in Kano State in Nigeria
(University Of Ghana, 2022-05) Adamu, I.
Tuberculosis (TB) is an infectious disease that has been considered as a signi_- cant risk factor that causes ill health. Globally, it has been found to be among the top 10 causes of death and ranks above HIV/AIDS as a single infectious agent that causes death in patient. Many researches have been documented using semiparametric and non-parametric models to analyze survival data in Nigeria. There is dearth of studies on the use of parametric models on tuberculosis survival data. Parametric models such as Weibull, Exponential, Log-logistic, Gompertz etc have been used in various studies to analyze data and Weibull was mostly found to be suitable. The popular non-parametric and semi-parametric tests used in various studies include the K-M, Log rank and Cox Proportional hazard model. However, necessary diagnostic checks on model _tness and non-violation of assumptions were mostly ignored. This reduces the reliability of result and increase chance of estimation error. This study assessed the parametric and semi-parametric model of survival such as Cox Model, Weibull, Exponential and Gompertz Models. A retrospective cohort analysis was conducted on the tuberculosis patients receiving treatment under the Tuberculosis & Leprosy Control Program in Kano, Nigeria. The risk factors for death were assessed using the Cox proportional hazard model. The risk factors for death were assessed using the Cox proportional hazard model. The parametric models were compared, and the gompertz model was found to be the best _t for the data based on its minimum AIC & log-likelihood value. Among 2,555 the TB cases, the success rate of TB treatment was 97.06% and the mortality rate was 2.94%. Multivariate analysis showed that HIV, Age & Weight were signi_cant factors associated with mortality in TB patients during therapy. The study recommends the use of diagnostic checks such as Martingale, Deviance Residuals in model _tness. Also, comparism of parametric models is recommended in determination of best model that _ts tuberculosis data of patients. Key words: Survival Analysis, Kaplan Meier, Cox Proportional Hazard Model, Parametric Models, Tuberculosis.
Modelling The Impact Of Political Stability On Cocoa Production
(University Of Ghana, 2019-12) Oforiwaa, P.
Economic growth and political stability are genuinely interrelated. In Ghana, the Cocoa Production Sector is one of the main boosters of the GDP. This paper used political stability as major intervention on the cocoa production. It sought to estimate and assess the impact of Political Stability as a variation on Cocoa Production in Ghana using Bia and Tiao, intervention analysis model. Time series data on cocoa productions from the department of Monitoring, Research and Evaluation of Ghana COCOBOD spanning from the year 1968 to 2016 was used. The Empirical result indicates that, the pre- intervention period was modeled with ARIMAX process based on which the full intervention model was obtained. The intervention event exists but it has an insignificant impact on cocoa production. The Ljung- Box test and its residual plots were significant. It concluded that the insignificant of political stability on cocoa production means that there is no influence of political appointees on the cocoa production. The study recommends that, the cocoa production sector should be independent of political interference since it’s the back bone of Ghana’s GDP.
Credit Card Fraud Detection; A Machine Learning Approach
(University Of Ghana, 2020-11) Glah, J.
In recent times, credit card usage has increased tremendously because it is convenient to use and also saves a lot of time. Credit cards are rectangular plastic cards issued by banks which allow a person to borrow funds from a pre - approved limit to pay for one’s purchases now and pay later. In the same manner, credit card frauds have also been on the increase causing huge sums of financial loss to credit card issuers. Credit card fraud is the use of a credit card by someone who is not the owner of the card and is not allowed to use it. In this study, three classification methods were used to do a deep analysis of credit card transactions history and the fraud detection models built. This study presents and demonstrates the advantages of support vector machine, artificial neural network and the k - nearest neighbor algorithms to the credit cards data for the purpose of reducing the bank’s losses. The results show that the linear support vector machine and k - nearest neighbor approaches outperform artificial neural network in solving the problem under investigation. This study allows for multiple algorithms to be integrated together as modules and their results combined to increase the accuracy of the final results.
Determining Premium In An Excess-Of-Loss Reinsurance Contract -An Extreme Value Approach
(University Of Ghana, 2022-06) Adams, S.
Statistics of extremes deals with the estimation of rare events that may have catastrophic effects on life, environment, among others. Since the introduction of Extreme value theory (EVT), it has been used in modelling various extreme events in fields such as finance, insurance, transportation, etc. In this thesis, the EVT is applied to model two claims datasets from the Ghanaian insurance industry. To do this, we employ the Peak Over Threshold (POT) method using the splicing Generalized Pareto Distribution (GPD) in modelling the tails of the underlying distributions. The primordial parameter in the estimation of extreme events is the tail index or Extreme Value Index (EVI). The EVI enables the classification of the underlying distribution of a dataset into three family of distributions that have short, light, or heavy tails. Thereafter, any of the parameters of extremes such as extreme quantiles, small exceedance probabilities, right endpoints and return periods can be estimated. Excess Loss Premium (XLP), Expected Shortfall (ES) and Value at Risk (VaR) as risk measures were thereafter calculated through the splicing method. The impact of the extreme value index (EVI) on these risk measures for the two datasets are discussed and suggestions made on how these could help the primary insurer in limiting the danger of large claims on the solvency of these companies. Based on this, the insurance companies can assess the risk associated with large claims and transfer some of these risks to reinsurance companies given their retention level. This study recommends that the splicing method should be used in fitting insurance data which behaves differently at various intervals of claims amount.
An Investigation Into Modeling Non-Life Insurance Claims In The Nigerian And Ghanaian Insurance Market
(University Of Ghana, 2022-04) Ringim, M.N.
For calculating non-life insurance premiums, actuaries rely on separate modeling of frequency and severity using covariates to explain the claims loss exposure. In this thesis, we focus on the insurance claims severity amount. Two separate insurance claims data were analyzed using some selected Tree-Based Machine Learning (ML) Algorithms namely; the Classification and Regression Tree (CART), Random Forest (RF), and Gradient Boosting (GB) Models. The predictive performance of the selected models were compared using the Coefficient of determination (R2), Mean Absolute Error (MAE), and Mean Squared Error (MSE). In the application of the selected models, this Thesis relied on two different insurance claims data; The Nigerian and the Ghanaian Insurance claims dataset. The Nigerian dataset had 10,017 observations from paid claims with 4 explanatory variables, while the Ghanaian dataset had 5,495 observations with 7 explanatory variables. In the analysis, 70% of the data were used for training and 30% for testing. Both datasets were compared in terms of the selected performance measures. The results show that the Random Forest model of the claims amount had the overall best performance for both Nigerian and Ghanaian Dataset.
Modelling Covid-19 Transmission In Ghana Using A Discrete-Time Markov Model And Machine Learning Time-Series Forecasting Algorithms
(University Of Ghana, 2022-09) Koduah, P.P.
The COVID-19 pandemic has and continue to have a severe impact on the health sectors, businesses, economies, and the world at large, despite many healthcare interventions, with much still yet to be learnt regarding its infection dynamics. In addition, researchers have developed classical compartmental or epidemiological models and other advanced mathematical models to better explain COVID- 19 infection dynamics across many countries. Critical information, such as the likelihood of first infection and recovery, average infection duration before this infection dies out entirely, COVID-19 infected people's life expectancy, and generalised transition probabilities, is understudied at any given future time. Using nationwide aggregated COVID-19 datasets and a discrete-time Markov model (to estimate these key disease metrics), the current study adds to our understanding of COVID-19 infection dynamics in Ghana. Additionally, the predictive power of some existing state-of-the-art machine learning (ML) algorithms such as K-Nearest Neighbor regression (KNN), Neural Network Auto-Regressive (NNAR), Generalized Regression Neural Network (GRNN), Multi-Layer Perceptron (MLP), and Extreme Learning Machines (ELM) in forecasting daily cases of COVID-19 infection (over the study period) is investigated using an out-of sample rolling-origin evaluation by exploring the trade-o_ between computational speed and accuracy. It was estimated that there would be a prolonged COVID- 19 transmission for at least 150 years before infection could die out. The study supports the idea that with a high overall recovery rate, a low infection rate, and a longer infection period, there is a possibility of herd immunity (as evident in the 2021 infection period despite the relatively high overall rate of infection). Finally, the K-Nearest Neighbour (KNN) regression was found to be the most cost-effective ML algorithm to predict the daily cases of COVID-19 in Ghana via the rolling-origin evaluation strategy.
Adopting Zero Inflated Models For Claim Counts And The Gamma Regression Model For Claims Cost In Determining Actuarial Premiums
(University Of Ghana, 2022-04) Amenu, F.M.
Insurance is the exchange of risk by an insured person through the payment of premiums for financial protection and economic benefit. The problem is how premiums should be charged so as to keep the industry alive to perform this basic function of insurance. Because of the Bonus-Malus system, or Hunger for Bonus system (also called No Claim Discount), and deductibles, most claims are not reported by policyholders, causing the number of claims to be dominated by zeros, which leads to over-dispersion in the data. In modeling the claim frequency, the Zero-Inflated Poisson (ZIP) and Zero-Inflated Negative Binomial (ZINB) models were adopted. The Gamma regression model was used to fit the claims cost data. The claim frequency regression model that best fits the claim frequency with the Gamma model for the claims cost was combined in determining the actuarial premium. These models were numerically illustrated with data obtained from a major non-life insurance company in Ghana and French Motor Third- Party Liability data from https://www.kaggle.com/datasets/karansarpal/ fremtpl2-french-motor-tpl-insurance-claims. The score test demonstrated the inability of the Poisson model to appropriately model the claims data due to the inflation of zeros in the data. The ZIP and ZINB were both found to be superior to their conventional equivalents based on the Vuong test statistics. The ZIP was chosen as an appropriate model for analyzing claim frequency data for both the French and Ghanaian data based on the values of the AIC and BIC. The risk factors that were found to influence claim frequency and claim cost were discovered to be different when both datasets were used. It is recommended that a separate analysis of claim frequency and claim cost be conducted with claim frequency receiving a high rating power.
Modelling Insurance Attrition Using Survival Analysis – A Case Study Of Ghana
(University Of Ghana, 2022-05) Asare, M.J.
Life insurance operations immensely contributes to the economic growth and development of a nation while also serving as an alternative form of internal fund mobilization for developing economies. This notwithstanding, life insurance companies tend to face challenges. One of these challenges they face is insurance attrition. This condition arises when insurance policies are terminated by the insurer as a result of discontinuation of premium payment after a specified period of time called the grace period, and also by the policy holder. Many factor(s) contribute to insurance attrition. The study focused on the length of survival time to attrition and the covariates that are likely to influence attrition. Randomly selected data was used in the study. Data was provided by an insurance company in Ghana for the period May 2018 to April 2021. The study employed Kaplan-Meier estimators, log-rant test and Cox regression model for the analysis of data. The study revealed the survival time of a new client is 16 weeks after subscribing on to policy. It also revealed assuming a three year period, attrition will occur after 15 weeks of being in force. The study concludes that marital status, product type, base rate change, deduction source are the factors that influence insurance attrition in Ghana.
Revisiting The Application Of Extreme Value Theory To The Management Of A Hydroelectric Dam
(University Of Ghana, 2023-06) Annor, E.
The Akosombo hydroelectric dam accounts for over a third of the electricity generation in Ghana. The amount of electricity produced depends on the amount of water in the dam. Therefore, studying the tail behaviour of the dam’s water level is crucial given the country’s rising demand for energy and the strain that this increased demand places on the dam. For engineers and coastal development planners, determining the likelihood that the water level of the Akosombo dam may rise due to heavy rains is crucial as it can lead to flooding. In this study, Extreme Value Theory was to model the tail behaviour of the water levels of the Akosombo dam. Truncation which is introduced naturally by the height of the dam was incorporated. The possibility of exceeding high-water levels that could cause flooding and its effects, as well as their associated return periods were also estimated. An evaluation of the dam water level data’s domain of attraction served as the study’s starting point. The data were fitted using the Generalized Extreme Value distribution (GEV) and the Generalized Pareto distribution (GPD). To account for potential truncation at very high-water levels, the Right-Truncated Peaks-Over-Threshold (RT-POT) Distribution was fitted to the data. The parameters of the GEV and GPD distributions were estimated using the Maximum Likelihood (ML) and Bayesian estimation methods. The parameters of the RT POT distribution were also estimated using the Maximum Likelihood (ML) and Hill estimation methods. The results show that Akosombo dam water level data tail distribution has a negative shape parameter (γ < 0), which places it in the Weibull domain of attraction. Both estimation methods yielded remarkably similar estimates. Several exceedance probabilities for various levels of the dam are also estimated. The results show that it is not conceivable for the dam’s water level to rise over its 278-foot maximum operating water level. Therefore, it is very unlikely for the water level to rise above the crest of the dam under the prevailing operating conditions.
Estimation Of Long-Run Probability Of Zero Offspring Using Branching Processes In Varying Environment
(University Of Ghana, 2022-04) Aidoo, E.K.
There are many challenges associated with both young and ageing population. If a country experiences a younger population, there’s a tendency for high unemployment rates and social vices. On the other hand, an ageing population typically results in a low labour force and high dependency ratios. Countries that tend to solve the problem of a young population initiate policies to control birth rates. However, these policies gradually lead to an ageing population before being revised, due to high costs associated with regular monitoring of population dynamics. Therefore, there is a need to develop a less costly method to monitor population dynamics and estimate the expected time to revise population policies. This study employed a more general theorem and a corollary based on ideas of probability generating functions in a branching process to come out with a method to solve the problem. The method was applied to both hypothetical and empirical data in the branching processes. The empirical data were obtained from Demographic and Health Surveys (DHS) for seven selected countries. The results from the study revealed that under certain closeness conditions, both constant and random environments yield similar results. Hence, using the method under the constant environment, which is easier, is a step in the right direction; otherwise, the proposed method for the random environment should be used. Burkina Faso recorded the youngest population, while Philippines recorded the least country with younger population. Results from the spectral analysis estimated that population policy for the selected countries should be revised between 34 to 40 years. The study recommended that the proposed model should be used to monitor population dynamics regularly. Also, population policies should be guided by appropriate time frame depending on the country’s demographic characteristics.
Large Deviation Principles For Empirical Measures Of Signal To Interference Noise Ratio (SINR) Graph
(University Of Ghana, 2022-11) Sakyi-Yeboah, E.
We obtain a Large Deviation Principle (LDP) and Asymptotic Equipartition Property (AEP) for Critical, Super-critical and Sub-critical telecommunication network modelled as SINR random network. Given devices space D, an intensity measure _m 2 R+ is a transitional kernel Q from the space D to positive real numbers R+ and a path loss function. The study defines a Marked Poisson Point Process (MPPP). For a given MPPP and technical constant __; _ : (0;1) ! (0;1); the study defines a Marked SINR Network as a Telecommunication Network and associate it with two empirical measures; the empirical marked measure and the empirical connectivity measure on two different scales as _2a_ and _, on a topological space, where _ is the intensity measure of the PPP which defines a SINR random network. For the class of telecommunication networks, the study proves a joint LDP for the empirical measures of the telecommunication network. Using this joint LDP, the study proves Asymptotic Equipartition Property (AEP) for the stochastic telecommunication network modelled as the marked SINR network. In addition, the study proves a Local Large Deviation Principle (LLDP) and a classical McMillian Theorem for the stochastic SINR network process. Further, for a typical empirical paired measure, we deduce from local large deviation principle a bound on the cardinality of the space of marked SINR network. Note that, the LDP for the empirical measures of this stochastic SINR network modelled as Telecommunication network was derived on space of measures equipped with the _􀀀 topology, and the LLDP were deduced in the space of the SINR model process without any topological restriction. All our rate function are expressed as relative entropies of the marked SINR on the device space D.
An Application Of Markov Chains And Mixed Poisson Distribution In Modelling No-Claim Discount Systems For Motor Insurance Data
(University Of Ghana, 2022-05) Akuminge, C.N.
Most No-Claim Discount (NCD) systems are unfair to either one or both parties. Most systems are the simple random walk model, whereby in case of a claim, the policyholder moves down a discount level and vice versa. Modelling of data of claim amount is of paramount importance to manage risk reserve for payment of claims. Actuaries model uncertainty using probability distributions. The movements within the NCD systems are those of the in-between cases, and a fair NCD system, should take into consideration the frequency of claims and the non-homogeneity factor. In this study, the Markov chains have been employed to explain the movement between levels in the NCD system and mixed Poisson distribution to calculate the probabilities, with the mixing distributions been the exponential and the gamma, and Poisson models. The motor insurance claim data from Sweden was used in this study. The study found that the Geometric distribution model was better fitted to the observed claim frequencies in both the maximum likelihood estimation and method moments than the Poisson model. The results for the 3-Level NCD systems showed that the policyholders were rewarded with approximately 95% chances of moving to the next higher level towards attaining a no premium zone if a claim is not made in the cycle and were punished if a claim is made by dropping to the lower level with approximate probability of 0.048 and it was generally observed. The study found that due to the fairness of the system, policyholders who make claims are equally punished by dropping from their current level to the lower one or are made to stay in their current level in the next cycle. In conclusion, the multi-level NCD system was designed to reward policyholders who are extra vigilant on the road in terms of avoiding road accidents and penalized bad road users. The descriptive statistics of the claim frequency revealed that the number of claims by policyholders was right or positively skewed with a mean number of claims approximately zero (0.053).
Statistical Assessment of the Performance of Dwt-Pca/Svd Recognition Algorithm on Reconstructed Frontal Face Images
(University of Ghana, 2020-11) Essah, B.O.
Face recognition is the second most important biometric part of the human body, apart from the biometric nger print. Detecting and measuring half face image processing or pattern recognition is a challenge in this eld. The research made use of Discrete Wavelet Transform (DWT) as the preprocessing mechanism and adopted the Principal Component Analysis and Singular Value Decomposition (PCA/SVD) for feature extraction and recognition. Numerical assessment of the performance of the adopted recognition algorithm gave average recognition rates of 95% and 75% when left and right reconstructed face images are used for recognition. Statistical analysis using the Wilcoxon Sign Rank test shows that, there is no signi cant di erence in the left and right reconstructed half face images when DWT-PCA/SVD is used for recognition. In conclusion, DWT-PCA/SVD is therefore recommend as one of the best noise viable algorithm for recognizing face images under partial occlusion.
The Effect of Moral Hazard on the Credit Risk in the Microfinance Sector; A Theoretical Approach
(University of Ghana, 2020-11) Aidoo, B.
Credit risk is a major concern in the banking and nance sector and has been one of the reasons for credit market imperfections across the globe. Moral hazard in credit markets, causes a major impact and a ects the determination of interest rates in the banking sector. This study set out to ascertain the probability of defaults of unsecured assets and secured assets. The study calculates the probability of occurrence of the behavior of borrowers and nd moral hazard e ects on individual credit risk system. Essentially, the study sought to nd how micro nance institutions are a ected when customers default on their payments. The study assessed the risk associated with micro nance business when the asset follows the Ornstein- Uhlenbeck process. Due to the fact that risks cannot be assessed using numerical data because we are dealing with human behaviors, we assumed that they invest their money in secured and unsecured assets. The study found that the impact of credit default was lesser with secured assets than it was with the unsecured assets and therefore recommend that micro nance institutions give credits with collateral more than the ones without collateral.
Stochastic Loss Reserving with Individual Claim Size Modeling
(University Of Ghana, 2019-07) Bolnaba, Y.M.
This study demonstrated the application of chain ladder, Bornhuetter-Ferguson, Mack model, probability and other statistical models in exploring loss reserving and claim behavior. Secondary data sets from an insurance company in Ghana were used for analysis and deductions. The focus of this research was to determine the probability distribution for the claims, fit the basic reserving methods (Chain-ladder, Bornhuetter- Ferguson) and juxtapose that with the Mack model with the help of basic stochastic assumptions. The research was peaked by determining the suitable model among the three models used for the available data. The chain ladder revealed that an amount of GHC 56,547,882 must be reserved while the Bornhuetter-Ferguson estimated an amount of GHC 230,516. Finally, the Mack stochastic model suggested that the latest payment should be GHC 30,008,300.16 with a development of 20% across the development years. The model also proposed that the ultimate and IBNR claims reserves should amount to GHC 149,758,939.87 and GHC 119,756,639.71 respectively. The behavior of the claim payment was known to follow a log-normal distribution. It was established that the Mack model was very robust as compared to other models. Future research should expand their application to bootstrapping for modeling of various parameters and reserves. A contingency fund must be created by insurance firms to suffice for payment in case there is a catastrophic event.
Modeling Tuberculosis Transmission Dynamics in the Ashanti Region of Ghana
(University of Ghana, 2019-07) Affi, P.O.
In attempt to model tuberculosis epidemic in the Ashanti Region of Ghana, SIR and SEIR deterministic and stochastic epidemiological models with demographic characteristics were employed. Both models showed success in modeling the infection dynamics of tuberculosis in the region. These models equilibrium points were established and their stability investigated through the Routh - Hurwitz stability criterion. The models predicted tuberculosis dying out in the entire region (Disease free equilibrium point stable) and an outbreak in Obuasi municipal and Amansie West district (endemic equilibrium point stable). It was revealed that SEIR model is the ideal model for modeling tuberculosis epidemic in the region since it characterized the infection dynamics of tuberculosis; the initial condition of the exposed compartment has influence on tuberculosis infection dynamics. Also, the branching process approximation of the epidemic revealed that there is a probability of one (1) for TB to be extinct or die out in the entire region. This was confirmed by the values of the thresholds: Malthusian parameter and the average number of offspring in a single generation. Sensitivity analysis was performed to investigate the impact of the model parameters on the reproduction number and it brought to light that increasing the infection and exposed rates increases the reproduction number while increasing the recovery/removal rate decreases the reproduction number. Finally, numerical simulations were done to validate the empirical results obtained and it revealed that all empirical estimates are good approximations for studying TB infection dynamics in the region.
Survival Analysis of Patients’ Length of Hospital Stay: A Case Study at the Legon Hospital, University of Ghana, Accra.
(University Of Ghana, 2019-07) Angkyiire, D.
Patient‟s duration of stay at the hospital is one useful indicator many employ to assess the performance and efficiency of healthcare provided by hospitals and healthcare units. Also, patients‟ LOS and inpatient mortality are two interconnected health issues with complex outcomes, and studying the relationship between the two is not an easy task. This study therefore employed non-parametric and semi-parametric statistics in modeling patients‟ survival time to death using secondary data from the Legon Hospital, university of Ghana, Accra. In the data analysis, we modeled patients‟ survival time to death by applying the Kaplan Meier survival model and Logrank test for equality of survival curves. Factors that are significant by the Logrank test are subjected to Cox PH regression analysis to determine their associative effect to relative hazards of patients‟ survival time to death at the hospital, within the study period. A summary of the results revealed that out of a sample of 532 patients used for the study, 394 events of interests (deaths) occurred within the study period with a mean duration of hospital stay as 6.8 days with prevalence and incidence rates of 74.06% and 10.88%, respectively. The Logrank test and Cox PH analysis revealed that age, cause of death and type of disease are valid predictors of patients‟ survival time to death, whereas regression analysis by cause of death reported that infectious diseases, cancers, respiratory disorders, diseases of blood and blood forming organs, and genitourinary diseases are significant predictors of the relative hazards of patients‟ survival time to death at the Legon Hospital, University of Ghana, Accra.
Application of Bühlmanns-Straub Credibility Theory to Claim Histories of Non-Life Marine Insurers in Ghana
(University of Ghana, 2019-07) Adjorlolo, P.K.
The study sought to demonstrate how credibility claim costs without the consideration of claim frequency and claim severities underlined by different risk profiles underestimate claim costs or premiums charged policyholders by non-life insurance companies. We used secondary data of non-life marine insurers in Ghana, claim histories that range from the period of 2013 to 2018. The claim histories included claim sizes, claim counts and policy counts. Bühlmans-Straub Credibility theory model was used in estimating credibility weights, credibility claim costs, credibility claim frequencies and credibility claim severities and subsequently find the credibility frequency-severity claim cost as the product of credibility claim frequency and severity for the individual and respective risk classes. We compared the estimates of the claim costs or premiums and have observed that the credibility claim costs underestimates claim costs or the average claim costs compared to the credibility frequency-severity claim costs for most of the risk classes. This is an indication of how a lack of consideration for variability or unstableness of claim frequencies and severities with different risk profiles undermine claim costs estimated through credibility rate makings in insurance. The study recommends that credibility ratemaking by insurance companies based on inadequate claim history and or with enough class risk variation should include credibility risk frequency and severity for the determination of credibility risk premiums.
Effects of Dependent Claims on the Probability of Ruin, The Time to Ruin Given Ruin Occurs
(University of Ghana, 2019-07) Sefa, A.M.
Ruin basically occurs to an insurance company when the claims paid out supersedes its initial capital and total premiums accumulated. In the classical theory of risk, the surplus is a significant model that deals with how long an insurance company's capital or surplus evolves. The first time ruin occurs is very crucial and the business must try to prevent it from happening again because it makes the business inefficient and inoperable. The time to ruin is so much a function of the initial capital and the way in which the insurance company's business books are priced. An insurance company has no control over how claims are issued, can attempt and handle its excess to assess the number of claims that will arise over time. The hypothesis that individual claims occur separately is one of the assumptions of the excess method. But this premise of independence is no longer true and sensible, as individual risks are generally homogeneous and share comparable features that claims from one eventuality could cause claims from another. In this thesis, the impacts of dependent claims on the likelihood of ruin and the time-to-ruin was examined also proposed premium adjustment when there is claim dependence. the objectives of this study is to determine how dependent claims, affect the likelihood of ruin and time to ruin of insurance companies in Ghana. And also to determine the time left for an insurance company to go to ruin when the assumption of dependency claims hold. The study employed Pollaczek-Khinchine formula, which was used to estimate probability of ruin and time to ruin, copulas and Pearson correlation was used to determine claims dependence. The study found out that the moment of ruin occurs more quickly in the presence of dependent claims. Therefore, the study recommended an adjustement of premims to hedge against negative cash flows in the assumption of claims dependent.

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