2004, Vol.15, No.3

Journal of Insurance and Finance 2023 KCI Impact Factor : 0.59

pISSN : 2384-3209
https://journal.kci.go.kr/kiri

If a market interest rate that is in an unstable time series is used as a reference interest rate to calculate the assumed interest rate, life insurers cannot avoid facing interest risk due to the difficulties of forecasting future long-term interest rates. Thus, it is necessary to determine an alternative method to calculate the assumed interest rate. In this study, we investigate a new method to calculate the assumed interest rate based on the average of the time series of returns on total assets of life insurers. The trend of the time series of returns on total assets of life insurers is stable after April 2004, when there was rapid systematicchange. Also, the size of variance of the returns on total assets of life insurers is about 50 % of that of the market interestrate. Therefore, we can tell that the return on total assets is better than the market interest rate as a reference interest rate in reducing the risk caused by determining the assumed interest rate.

This paper analyses the Korean National Pension system through the actuarial model that is the standard practice of private insurance, though recognizing its fundamental limitation caused by complicate benefit systems and deficient related basic rates. The specific actuarial model constructed is a joint life annuity model with invalid benefits. The core of model is the estimation of expected contributing years using the concept of curtate life expectancy. Based on this model with a representative male entering the system at the age of 28 with three year younger wife, this paper estimates the actuarial structure of Korean National Pension system. The size of survivors benefit is estimated to be in the range of 9.2% - 10.5% depending on the discount rate of total benefit and the size of invalid benefit is estimated to be in the range of 2.1% - 2.9% much smaller size than that of survivors benefit. The remaining 86.5% - 88.7% pertains to the old age benefits. Thus all existing studies can be said to underestimate the benefits by 11.3% - 13.4% virtually omitting the survivors and disabled benefits.

This study follows up the earlier works of Haberman & Sung (1994, 2002, 2004) who have adopted a dynamic approach to pension funding in order to control and harmonize simultaneously the contribution risk and the solvency risk, based on a linear stochastic dynamic system with a quadratic optimisation criterion (LQP problem). In contrast to these earlier works, we here consider funding plans for defined benefit mature pension schemes where the spread method is used to eliminate the solvency surpluses and deficiencies evaluated in relation to their own expecting funding targets. Moreover, we consider the infinite-time, non-stationary LQP optimisation control problem due to trending non-stationary rates of return, which is a theoretical extension of Sung (2003) dealing with deterministic approach. We note that it is insoluble but propose a heuristic optimisation procedure for solving this problem and then illustrate with a specific numerical projections of contribution and solvency risks.