Print Email Facebook Twitter Examination of insurer fees by means of life expectancy Title Examination of insurer fees by means of life expectancy Author Verkade, W.J. Contributor Kurowicka, D. (mentor) Faculty Electrical Engineering, Mathematics and Computer Science Department Applied mathematics Date 2014-08-25 Abstract In the Netherlands, the pension regulation consists of three pillars. The first pillar consists of the basic state pension called AOW (algemene ouderdomswet), which is meant to provide a financial foundation for every person. At the moment, the yearly AOW contribution for a retired person is somewhere between 10.000 and 15.000, depending on whether or not you have children or a partner with income. The second pillar is meant for every employed person as an addition to the AOW pension. Mostly, the employer has an agreement with an insurer, to which he pays a yearly premium for every employee. The insurer then pledges the employee a pension at retirement, amount of which is based on the yearly premium. This premium is partially paid by the employee's salary and partially by the employer. So the employee actually sets aside a part of salary to save for his pension. Every employer has its own regulation for this secondary term of employment. It is however legally obligatory. The third pillar consists of every other form of building up pension. For example, depositing money into a bank or taking additional insurances. In this report we will only examine the second pillar. For convenience, we shall simply call this second pillar; pension. The insurers costs of providing a pension depends on how much and long a person will receive a pension as well as how long this person saves for his/her pension. The goal of this research is to investigate how the main insurers in the Netherlands determine their costs of providing a pension. We will examine two main algorithms that are used to determine insurersâ€™ premium, discuss assumptions used in these algorithms and investigate whether these assumptions are reasonable. The report is organized as follows: First, we discuss the general approach how insurers calculate their premiums which are based on the estimated future expenses of the insurer. The future expenses of a person are determined on basis of how long this person is going to live after his retirement and the interest rates. To calculate how much a person has to pay now to receive a certain amount of pension in the future, the calculated expenses are discounted. Since the money put aside now could be invested, it is worth now less than it will be worth in the future. Discounting requires the choice of the interest rate. This discount rate is based on the expected return of risk-free investments such as government bonds. Because the discount rate have a huge impact on the premium, we will discuss it in this report in Section 2. Every person is different, so the insurer has to estimate the expected life length of a person after retirement. In section 4 the life expectancy is calculated using mortality rates, which provide the probability of death at a certain age. The data about the historical mortality rates of Dutch population is available. However, to calculate future expenses the insurers need the future mortality rates rather than the historical ones. Hence the future mortality rates have to be forecasted. We will examine two algorithms that allow to forecast mortality rates and provide the life expectancy curves that can be obtain with these forecasted mortality rates. In Section 5 the the Royal Actuarial Association (AG) is presented. Section 6 contains explanation of the PLT model (pensioenen lijfrentetafel workgroup). Both models use a similar approach based on the smooth historical data, which is extrapolated to determine a forecast of 50 years. The models do not contain uncertainty of the forecast. An alternative model is proposed by Central Bureau of Statistics (CBS). The CBS model is different from the other two. It is a lot more complex as it includes causes of death and takes medical developments into account. Besides that, it does give an indication of the uncertainty in the forecast, which is a nice advantage. However, due to its complexity, it will not be investigated in this report. Section 8 contains comparison of fees that the insurers use to cover their future expenses. Insurer fees are essentially the premiums for buying 1 euro of pension of an insurer. Insurers determine these fees based on their own methods. Some just use the forecast of one of the earlier mentioned models, while others do their own calculations. Since the fees would be different for each employee in general the simplified calculations are performed by insurers. Instead of looking at every employee separately, the insurers calculate fees for the employee with average age. We will see how these simplified calculations compare to previously discussed ones. Finally we conclude the report and provide the recommendation. The detailed presentation of algorithms discussed in this report are shown in Appendices. Moreover R-code used to make figures and obtained results included in this report is included in the end. Subject pensioninsurancelife expectancyfees To reference this document use: http://resolver.tudelft.nl/uuid:d2284a99-9598-4189-a037-1961caad0009 Part of collection Student theses Document type bachelor thesis Rights (c) 2014 Verkade, W.J. Files PDF Examination_of_insurer_fe ... ctancy.pdf 2.62 MB Close viewer /islandora/object/uuid:d2284a99-9598-4189-a037-1961caad0009/datastream/OBJ/view