(R1503) Numerical Ultimate Survival Probabilities in an Insurance Portfolio Compounded by Risky Investments

Probability of ultimate survival is one of the central problems in insurance because it is a management tool that may be used to check on the solvency levels of the insurer. In this article, we numerically compute this probability for an insurer whose portfolio is compounded by investments arising from a risky asset. The uncertainty in the celebrated Cramér-Lundberg model is provided by a standard Brownian motion that is independent of the standard Brownian motion in the model for the risky asset. We apply an order four Block-by-block method in conjunction with the Simpson rule to solve the resulting Volterra integral equation of the second kind. The ultimate survival probability is arrived at by taking a linear combination of some two solutions to the Volterra equations. The several numerical examples show that the results are accurate and reliable. The method performs well even when the net profit condition is violated

Dividend Maximization Under a Set Ruin Probability Target in the Presence of Proportional and Excess-of-loss Reinsurance

We study dividend maximization with set ruin probability targets for an insurance company whose surplus is modelled by a diffusion perturbed classical risk process. The company is permitted to enter into proportional or excess-of-loss reinsurance arrangements. By applying stochastic control theory, we derive Volterra integral equations and solve numerically using block-by-block methods. In each of the models, we have established the optimal barrier to use for paying dividends provided the ruin probability does not exceed a predetermined target. Numerical examples involving the use of both light- and heavy-tailed distributions are given. The results show that ruin probability targets result in an improvement in the optimal barrier to be used for dividend payouts. This is the case for light- and heavy-tailed distributions and applies regardless of the risk model used

On the multiplicity in Pillai\u27s problem with Fibonacci numbers and powers of a fixed prime

Let ( {F_n}_{ngeq 0} ) be the sequence of Fibonacci numbers and let (p) be a prime. For an integer (c) we write (m_{F,p}(c)) for the number of distinct representations of (c) as (F_k-p^ell) with (kge 2) and (ellge 0). We prove that (m_{F,p}(c)le 4)

Drivers of potential policyholders’ uptake of insurance in Kenya using Random Forest

The low adoption of insurance by potential policyholders in developing countries like Kenya is a cause for concern for insurers, regulators, and other marketing stakeholders. To effectively design targeted marketing strategies to boost insurance adoption, it is crucial to determine the factors that affect insurance uptake among potential policyholders. In this study, the 2021 FinAccess Survey, which interviewed sampled individuals above 16 years in Kenya and machine learning techniques, including Random Forest, XGBoost, and Logistic Regression, were utilized to uncover the factors driving insurance uptake and the reasons for the low adoption of insurance among potential policyholders. Random Forest was the most robust model of the three classifiers based on Kappa score, recall score, F1 score, precision, and area under the operating characteristic curve (approaching 1). The paper explores eight reasons why people currently do not have insurance policies. The results indicated that affordability was the primary driver of uptake with 68.67% of having expressed a desire to possess insurance but are unable to afford it. The highest level of education being the next most significant factor. Cultural and religious beliefs and mistrust of insurance providers were found to have a minimal impact on uptake. These findings imply that offering affordable insurance products and conducting awareness campaigns are critical to increase insurance adoption

The HIV-HCV co-infection dynamics in absence of therapy

Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, KenyaHIV-HCV co-infection is whereby an individual is infected with both viruses HIV and HCV. Globally, approximately 4 to 5 million people are co-infected with HIV and HCV. HCV infection significantly causes morbidity and mortality among HIV patients. HCV is known to progress faster and cause more liver-related health problems and death among people who are HIV/AIDS positive than those who are negative. Co-infection with HCV complicates the management of HIV/AIDS. Mathematical modeling generally provides an explicit framework by which we can develop and communicate an understanding of transmission dynamics of an infectious disease. In this article, a deterministic model is used in which ordinary differential equations are formulated and analyzed to study the HIV-HCV co-infection dynamics in absence of therapy. The findings reveal that the basic reproduction number for HIV-HCV co infection dynamics is equal to the maximum of single-disease basic reproduction numbers. This implies that the dynamics of the HIV-HCV co-infection will be dominated by the disease with the bigger basic reproduction numberInstitute of Mathematical Sciences, Strathmore University, Nairobi, Kenya. Uganda Virus Research Institute London School of Hygiene and Tropical Medicine, Ugand

Dependency Modeling Approach of Cause-Related Mortality and Longevity Risks: HIV/AIDS

Disaggregation of mortality by cause has advanced the development of life tables for life insurance and pension purposes. However, the assumption that the causes of death are independent is a challenge in reality. Furthermore, models that determine relationships among causes of death such as HIV/AIDS and their impact on mortality and longevity risks seem trivial or inflexible. To address these problems, we aim to determine and build an appropriate copula dependence model for HIV/AIDS against other causes of death in the presence of age, gender, and time. A bivariate copula model is proposed to capture the dependence structure of HIV/AIDS on life expectancy. This approach allows the fitting of flexible and interpretable bivariate copulas for a two-dimensional case. The dataset was derived from the World Health Organization database that constituted annualized death numbers, causes, age, gender, and years (2000 to 2019). Using Kendall’s tau and Pearson linear coefficient values, the survival Joe copulas proved to be a suitable model. The contribution and implication of this research are the quantification of the impact of HIV/AIDS on a life table, and, thus, the establishment of an alternative to the subjective actuarial judgment approach

Prediction of the Stock Prices at Uganda Securities Exchange Using the Exponential Ornstein–Uhlenbeck Model

We use the exponential Ornstein–Uhlenbeck model to predict the stock price dynamics over some finite time horizon of interest. The predictions are the key to the investors in a financial market because they provide vital reference information for decision making. We estimated all the parameters of the model (mean reversion speed, long-run mean, and the volatility) using the data from Stanbic Uganda Holdings Limited. We used the parameters to forecast the stock price and the associated mean absolute percentage error (MAPE). The predictions were compared against those by the ARMA-GARCH model. We also found the 95% prediction intervals before and during the COVID-19 pandemic. Results indicate that the exponential Ornstein–Uhlenbeck stochastic model gives very accurate and reliable predictions with a MAPE of 0.4941%. All the forecasted stock prices were within the prediction region established. This was not the case during the COVID-19 pandemic; the predicted stock prices are higher than the actual prices, indicating the severe impact COVID-19 inflicted on the stock market