title: Mathematical Perspectives on Insurance for Low-Income Populations
Creators: name: Henshaw, Kira
Publisher: name: University of Liverpool Repository
Year: 2022

description: In this thesis, insurance solutions for low-income populations and their capacity for poverty reduction are considered. Classical risk theory techniques are adopted to the study of the trapping probability, where "trapping" refers to the event at which an economic entity falls below the poverty line and into an area of poverty, from which it is difficult to escape without external help. In the poverty setting, the trapping probability mimics an insurer's probability of ruin. Studying two household-level capital processes that align with risk processes with deterministic investment and (i) random-valued and (ii) multiplicative claims, explicit trapping probabilities are derived. The ability of low-income insurance strategies to reduce trapping probabilities is assessed, with a particular focus on government subsidy schemes. For those closest to the poverty line, insurance without subsidies increases their probability of trapping in both the random-valued and multiplicative cases, in line with the existing literature. The governmental cost of social protection is reduced under subsidisation schemes, with a premium payment barrier strategy additionally ensuring the increased risk associated with insurance purchase is mitigated. Purchase of insurance for multiplicative losses is found to be more affordable than for random-valued losses. A stochastic dissemination model is proposed for the extension of the problem to the group setting, in line with the prevalence of risk sharing and group-based insurance schemes across low-income communities. Consideration of risk sharing suggests that the impact of loss and premium payment is shared throughout a homogeneous group, mitigating the severity of negative wealth transaction events. Subsidisation is also found to support both the insured and the uninsured, further highlighting the benefit of governmentally supported schemes. In the second part of the thesis, the existence of lifetime dependence and the influence of socioeconomic features on its structure are considered. Analysis is undertaken on data sets from Ghana and Egypt, with dependence induced through joint stochastic mortality and copula models, respectively. The impact of dependence on the pricing of a reversionary annuity is derived through implementation of the indifference pricing principle. In general, pricing under the dependence assumption decreases the indifference price of the annuity. In visualising both data sets, dependence is observed to be lower in this alternative socioeconomic environment than previously observed in the existing empirical literature, supporting suggestion of socioeconomic influences on bereavement processes. Studying the existence of pairwise dependence within relationships beyond the classical husband-wife case, dependence within child-parent relationships is also found to be significant. Accounting for this existence, even where reduced, is critical to improving the accuracy of insurance product pricing and to mitigate the mortality risks faced by insurers, particularly given the uncertain nature of the low-income financial environment.