Markov Chain Method for Calculating Insurance Premiums

Abstract

This study applies the Markov Chain method to calculate insurance premiums based on the dynamic health status of policyholders over time. The model considers three health states Healthy, Mild Illness, and Severe Illness each associated with a specific insurance premium. The transition probabilities between these states are represented in a transition matrix, capturing the likelihood of a policyholder remaining in their current health state or transitioning to another state in a given period. Using this approach, the steady-state distribution, which reflects the long-term probabilities of being in each health state, is calculated. This distribution is then used to determine the expected monthly premium by taking a weighted average of the premiums for each state. The methodology incorporates real-world scenarios where a policyholder's health condition may change over time, impacting the premiums they are required to pay. The Markov Chain model provides an effective framework for estimating these premiums by considering the "memoryless" nature of health state transitions, where future states depend only on the current state and not on prior health history. By solving the steady-state equations pi P=pi and ensuring the total probabilities sum to one, the model yields a robust estimation of long-term health state distributions. These distributions, combined with the associated premiums, produce an accurate calculation of expected insurance costs. The results demonstrate the flexibility and accuracy of the Markov Chain method in assessing risks and setting premiums. Insurers benefit from this approach as it enables dynamic pricing strategies tailored to individual risk profiles. For policyholders, the model provides transparency in understanding how health status influences premiums. Overall, this study highlights the practicality of using Markov Chains in health insurance pricing and underscores their importance in creating equitable and sustainable insurance systems.