Analysis of long-term disability insurance portfolios with stochastic interest rates and multi-state transition models

A general long-term disability insurance portfolio with semiannual disability payments and a lump sum death benefit payment is studied in this project. The transitions for policyholders in this portfolio, between the healthy, temporarily disabled, permanently disabled and the deceased statuses, are assumed to follow a continuous-time Markov process. The cash flow method is applied to study the first and second moments of the present value of future benefit payments and evaluate the total riskiness of the general insurance portfolio, which is decomposed into its insurance risk and investment risk. An alternative recursive method based on the term of the insurance policy is also demonstrated for the moment calculations of a single policy case. Two stochastic interest rate models, a binomial tree model and an AR(1) process, and a deterministic interest rate model are considered and illustrated.