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Abstract
We analyze the newly introduced German occupational pension scheme called target pension (“Zielrente”), which links the beneficiaries’ benefits during the retirement phase to the mortality experienced among the pension beneficiaries and the performance of the financial market, from a pension beneficiary’s perspective. We model the contract payoffs related to the target pension according to the new enhancement law on German occupational law. Specifically, we include two parameters in the plan design, one to control the surplus participation and one to control the loss participation. These parameters are chosen in such a way that the initial wealth of the retiree equals the initial value of the target pension. With the help of expected lifetime utility and wealth equivalent, we find that the target pension provides a meaningful supplement to the first and third pillar. Further, we find some comparative advantages of the target pension over the traditional pure defined benefit and some defined contribution plans from a policyholder’s point of view. Our analysis with reasonable parameter choices shows that target pension plans can be outperformed by defined contribution plans with variable annuities, while the latter are accompanied by a considerably higher ruin probability.
Highlights
One of the major societal challenges is the changing demographics due to our aging society
Our results suggest that a TP is likely to be a more benefi‐ cial occupational pension scheme than some defined contribution (DC) and defined benefit (DB) schemes, as the resulting wealth equivalents are below the initial wealth invested in the DC and DB schemes
To com‐ pare the resulting utility level of the TP to that of a conventional annuity with con‐ stant annual payments, we consider the wealth equivalent, which is the initial wealth level WE invested in the optimal TP which makes the retiree indifferent between the TP and DB scheme, where the initial value of the DB scheme is given by x0
Summary
One of the major societal challenges is the changing demographics due to our aging society. There are two objectives: (1) We want to find out whether a TP can be a meaningful supplement to the first and third pillar, and (2) whether the TP can bring some added value within the second pillar, especially compared to the DC and DB scheme To answer these questions, we assume that the retiree splits her initial wealth between some occupational pension scheme and a constant annuity resulting from the first and third pillar. To assess the added value which an individual gains by joining a TP scheme, we consider the wealth equivalent derived from the expected utility, which is the initial wealth level required for a TP to achieve the same expected utility level as some other pension scheme with some fixed initial wealth level In both model frameworks, we find that individuals with different degrees of rela‐ tive risk aversion invest positive fractions of their wealth in a TP, suggesting that the TP forms a meaningful supplement to the first and third pillar.
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