Critical illness insurance pricing with stochastic interest rates model

Abstract

In this paper, we will explain critical illness insurance calculations with stochastic interest rates. The survival model is multiple states, while the interest rate is the Cox-Ingersoll-Ross stochastic interest rate model. In determining the survival model, we use the prevalence and mortality rates of certain critical diseases, such as neoplasms, endocrine diseases, and diseases of the digestive system. Furthermore, the Monte Carlo simulation will be used to simulate the possibility of interest rate pathways in determining critical illness insurance premiums.

The Graduation of Transition Intensities From Semi-Markov Processes to Premium Pricing

“…Next, after the 𝛽 ̑𝑘 value is obtained, the graduation process continues. The link function for the Poisson distribution is log-link, then 𝜂 = 𝑙𝑜𝑔( 𝜆 𝑢 ) = 𝑙𝑜𝑔(𝑡 𝑢 ) + 𝑙𝑜𝑔(𝜇 𝑖𝑗 𝑢 ) = 𝑙𝑜𝑔(𝑡 𝑢 ) + ∑ 𝑥 𝑘𝑢 𝛽 ̂𝑘 𝑘 (18) 𝑙𝑜𝑔( 𝑡 𝑢 ) is the offset, namely an additional variable with a known regression coefficient of +1. So the transition intensity, 𝜇 𝑖𝑗 𝑢 is related to the covariate through the following relationship.…”

“…The graduation process is done with a Generalized Linear Model (GLM) [16], [17]. The integrated transition intensity estimator is used to form transition probabilities associated with the Kolmogorov Backward and Forward differential equations [18]. This estimator is ultimately used as one of the assumptions in determining health insurance premiums.…”