Subsidising Inclusive Insurance to Reduce Poverty

Abstract

In this article, we assess the benefits of coordination and partnerships between governments and private insurers, and provide further evidence for microinsurance products as powerful and cost-effective tools for achieving poverty reduction. To explore these ideas, we model the capital of a household from a ruin-theoretic perspective to measure the impact of microinsurance on poverty dynamics and the governmental cost of social protection. We analyse the model under four frameworks: uninsured, insured (without subsidies), insured with subsidised constant premiums and insured with subsidised flexible premiums. Although insurance alone (without subsidies) may not be sufficient to reduce the likelihood of falling into the area of poverty for specific groups of households, since premium payments constrain their capital growth, our analysis suggests that subsidised schemes can provide maximum social benefits while reducing governmental costs.

Figures (13)

• Figure 1: (a) Laplace transform $m_{\delta}(x)$ of the trapping time when $Z_{i} \sim Exp(1)$, $a = 0.1$, $b = 1.4$, $c = 0.4$, $\lambda = 1$, $x^{*} = 1$ for $\delta = 0, \frac{1}{8}, \frac{1}{32}, \frac{1}{128}$ (b) Trapping probability $\psi(x)$ when $Z_{i} \sim Exp(\alpha)$, $a = 0.1$, $b = 1.4$, $c = 0.4$, $\lambda = 1$, $x^{*} = 1$ for $\alpha = 0.8, 1, 1.5, 2$.
• Figure 2: Expected trapping time when $Z_{i} \sim Exp(1)$, $\lambda = 1$ and $x^{*} = 1$ for $r = 0.02,0.03,0.04$.
• Figure 3: (a) Laplace transform $m_{\delta}^{\scaleto{(\kappa)}{5pt}}(x)$ of the trapping time when $Z_{i} \sim Exp(1)$, $a = 0.1$, $b = 1.4$, $c = 0.4$, $\lambda = 1$, $x^{\scaleto{(\kappa)*}{5pt}} = 1$, $\kappa = 0.5$ and $\theta=0.5$ for $\delta = 0, \frac{1}{8}, \frac{1}{32}, \frac{1}{128}$ (b) Trapping probability $\psi^{\scaleto{(\kappa)}{5pt}}(x)$ when $Z_{i} \sim Exp(\alpha)$, $a = 0.1$, $b = 1.4$, $c = 0.4$, $\lambda = 1$, $x^{\scaleto{(\kappa)*}{5pt}} = 1$, $\kappa = 0.5$ and $\theta=0.5$ for $\alpha = 0.8, 1, 1.5, 2$.
• Figure 4: Trapping probabilities for the uninsured and insured capital processes when $Z_{i} \sim Exp(1)$, $a = 0.1$, $b = 1.4$, $c = 0.4$, $\lambda = 1$, $\kappa = 0.5$, $\theta=0.5$ and $x^{*} = x^{\scaleto{(\kappa)*}{5pt}} = 1$.
• Figure 5: (a) Trapping probabilities for the uninsured, insured and insured subsidised capital processes when $Z_{i} \sim Exp(1)$, $a = 0.1$, $b = 1.4$, $c = 0.4$, $\lambda = 1$, $x^{*} = x^{\scaleto{(\kappa)*}{5pt}} = x^{\scaleto{\pi(\kappa, \theta)*}{5pt}} = 1$, $\kappa = 0.5$, $\theta = 0.5$ and $\pi = 0.75$ for $\pi^{*} = 0, 0.55$ (b) Optimal $\pi^{*}$ for varying initial capital when $Z_{i} \sim Exp(1)$, $a = 0.1$, $b = 1.4$, $c = 0.4$, $\lambda = 1$, $x^{\scaleto{\pi(\kappa, \theta)*}{5pt}} = 1$, $\kappa = 0.5$, $\theta = 0.5$ and $\pi = 0.75$.

Theorems & Definitions (22)

• Definition 2.1
• Proposition 3.1
• Remark 3.1
• Remark 3.2
• Corollary 3.1
• Remark 3.3
• Proposition 4.1
• Remark 4.1
• Remark 4.2
• Proposition 5.1