Market-based insurance ratemaking: application to pet insurance

Abstract

This paper introduces a method for pricing insurance policies using market data. The approach is designed for scenarios in which the insurance company seeks to enter a new market, in our case: pet insurance, lacking historical data. The methodology involves an iterative two-step process. First, a suitable parameter is proposed to characterize the underlying risk. Second, the resulting pure premium is linked to the observed commercial premium using an isotonic regression model. To validate the method, comprehensive testing is conducted on synthetic data, followed by its application to a dataset of actual pet insurance rates. To facilitate practical implementation, we have developed an R package called IsoPriceR. By addressing the challenge of pricing insurance policies in the absence of historical data, this method helps enhance pricing strategies in emerging markets.

Figures (13)

• Figure 1: Pure premiums as a function of the rate of coverage (r) and the deductible (d) for a $\mathsf{Poisson}(\lambda = 3)-\mathsf{LogNorm}(\mu = 0, \sigma = 1)$ risk.
• Figure 2: Pure premium as a function of the commercial premium offered by various insurance companies.
• Figure 3: Contour plot of $\text{RMSE}(p_{1:n}, p_{1:n}^\theta)$ for $\mu = 0$ and $(\lambda,\sigma)\in [0,5]\times [0,2]$.
• Figure 4: Isotonic link between the pure and commercial premiums.
• Figure 5: Contour plot of $\text{RMSE}\left[\Tilde{p}_{1:n}, f\left(p^\theta_{1:n}\right)\right]$ and $d\left[\Tilde{p}_{1:n}, f\left(p_{1:n}^\theta\right)\right]$ for $\mu = 0$ and $(\lambda, \sigma) \in [0, 5] \times [0, 2]$.

Theorems & Definitions (10)

• Example 1
• Example 2
• Example 3
• Example 4
• Remark 3.1
• Remark 3.2
• Example 5
• Remark 3.3
• Example 6
• Remark 5.1