Mortality by socio-economic class and its impact on the retirement schemes: how to render the systems fairer?

Many OECD countries have addressed the issue of increased longevity by mainly increasing the retirement age. However, this kind of reforms may lead to substantial transfers from those with shorter lifespans to those that will live longer than the average, as they do not necessarily take into account the socio-economic differences in mortality. The contribution of our paper is therefore twofold. Firstly, we illustrate how both a Defined Benefit and a Notional Defined Contribution pay-as-you-go scheme can put the lower social economic classes at a disadvantage, when compared to the actuarially fair pensions. In contrast to that, higher classes experience a gain. This is due to the fact that mortality rates per socio-economic class are not considered by either scheme. Consequently, we propose a model that determines the parameters for each scheme and class which would render the pensions fairer even when no socio-economic mortality differences are considered.

Optimal investment strategies for pension funds with regulation-conform dynamic pension payment management in the absence of guarantees

In this article we consider the post-retirement phase optimization problem for a specific pension product in Germany that comes without guarantees. The continuous-time optimization problem is defined consisting of two specialties: first, we have a product-specific pension adjustment mechanism based on a certain capital coverage ratio which stipulates compulsory pension adjustments if the pension fund is underfunded or significantly overfunded. Second, due to the retiree’s fear of and aversion against pension reductions, we introduce a total wealth distribution to an investment portfolio and a buffer portfolio to lower the probability of future potential pension shortenings. The target functional in the optimization, that is to be maximized, is the client’s expected accumulated utility from the stochastic future pension cash flows. The optimization outcome is the optimal investment strategy in the proposed model. Due to the inherent complexity of the continuous-time framework, the discrete-time version of the optimization problem is considered and solved via the Bellman principle. In addition, for computational reasons, a policy function iteration algorithm is introduced to find a stationary solution to the problem in a computationally efficient and elegant fashion. A numerical case study on optimization and simulation completes the work with highlighting the benefits of the proposed model.

Dynamic surplus optimization with performance- and index-linked liabilities

The increasing importance of liability-driven investment strategies and the shift towards retirement products with lower guarantees and more performance participation provide challenges for the development of portfolio optimization frameworks which cover these aspects. To this end, we establish a general and flexible terminal surplus optimization framework in continuous time, allowing for dynamic investment strategies and stochastic liabilities, which can be linked to the performance of an index or the asset portfolio of the insurance company. Besides optimality results in a fairly general surplus optimization setting, we obtain closed-form solutions for the optimal investment strategy for various specific liability models, which include the cases of index-linked and performance-linked liabilities and liabilities which are completely or only partially hedgeable. We compare the results in numerical examples and study the impact of the performance participation, unhedgeable risk components, different ways of modeling the liabilities and the relative risk aversion parameter. We find that performance- or index-linked liabilities, which provide a close link between the wealth of the insurance company and its liabilities, allow for a higher allocation in the risky investment. On the other hand, unhedgeable risks reduce the allocation in the risky investment. We conclude that, aiming at a high expected return for the policy holder, insurance companies should try to connect the performance of insurance products closely to the wealth and minimize unhedgeable risks.