A variety of mortality models can be used to project future mortality. However, the parameters of most of these models lack a clear demographic interpretation. Hence, the resulting projections may be demographically implausible in the sense that trends in key demographic statistics are not extrapolated in a reasonable way. When demographers make predictions on future mortality, they typically focus on one or few relevant demographic statistics related to certain aspects of the mortality evolution. However, they do not derive comprehensive mortality forecasts as required for actuarial purposes. This article aims to close the gap between these forecasting approaches. To this end, we establish a new deterministic mortality model which can be used for best estimate and scenario forecasts. We model the deaths curve, i.e. the age-at-death distribution, and derive forecasts based on the extrapolation of statistics that have a clear demographic interpretation. The four key statistics of the model are those from the classification framework of Bo & uml;rger et al. (2018). The design of our model makes sure that forecasts for the immediate future of the deaths curve are consistent with the most recent trends of all demographically relevant statistics. Moreover, expert opinions with respect to the future trends of certain demographically interpretable statistics can easily be incorporated-in particularly for the farther future where a pure extrapolation of historic trends might lead to implausible results. We present a possible implementation of the model and provide case studies that illustrate how the model can be applied.

In traditional life insurance, typically return smoothing mechanisms are used to reduce the volatility of policyholders’ returns and provide risk sharing between policyholders. By analyzing two illustrative smoothing mechanisms, we demonstrate that different smoothing mechanisms may have different effects. We find that mechanisms that are purely based on average historical asset returns can significantly reduce pathwise volatility (intertemporal smoothing) but have hardly any impact on the standard deviation of terminal wealth. In contrast, mechanisms using buffers that are built up “in good years” in order to increase returns “in bad years” can—when properly designed—reduce the standard deviation of terminal wealth without reducing the ex ante expected return by means of intergenerational risk sharing. We conclude that simple generic mechanisms that are often used in academic papers may not fully cover the effects resulting from return smoothing. Our results indicate that—when properly designed—intergenerational risk sharing mechanisms can improve risk-return profiles but at the price of increased complexity and potentially lower surrender values. A strong regulatory focus on simple products and sufficiently high surrender values might disincentivize products with intergenerational risk sharing despite their positive effects.

Traditional life insurance typically uses some mechanism that is aimed at smoothing the returns of the (collective) assets in the insurer's so-called cover fund. We consider a generic smoothing mechanism and numerically analyze how it impacts the risk-return characteristics of a traditional life insurance contract distinguishing between pathwise volatility (of the annual returns) and the volatility of terminal wealth. We find that pathwise volatility is significantly reduced while the distribution of terminal wealth is hardly affected. We conclude that using multiple segregated cover funds (that come with different asset allocations) as building blocks for more complex products enables insurers to offer a variety of risk-return profiles of terminal wealth in combination with a rather low pathwise volatility (compared to investments without smoothing mechanism). This increases subjective attractiveness for a typical consumer. We consider a variety of such products (static and dynamic investment products) and compare them to similar purely market-based products that do not use an insurer's cover fund. Analyzing risk-return characteristics, (objective) utility, and (subjective) attractiveness under Cumulative Prospect Theory and extensions of it, we conclude that products that become possible by implementing multiple segregated cover funds can increase both, objective utility and subjective attractiveness.

For many life insurance companies, traditional life insurance with surplus participation is still a major portion of their business. As a consequence of the low interest rate environment, financial guarantees of new contracts have been decreased. Hence, new business reduces the average guaranteed rate of interest for the whole block of business. At the same time, however, new policyholders benefit from higher yields of assets in the existing asset portfolio built up with previous policyholders’ contributions. Therefore, it is not obvious whether new policyholders benefit from or subsidize the existing portfolio. In this paper, we use the collective bonus introduced in Eckert et al. (Eur Actuar J, 2020) to measure the interaction between new policyholders and the existing insurance portfolio. Considering the situation in Germany as an example, we measure and explain cross-subsidizing effects resulting from different cohorts of policyholders being linked to the same asset portfolio. In particular, we show under which circumstances there is a benefit for or subsidization from new business.

Standard economic models of rational decision making provide information on how people should decide. In practice, human decisions are influenced by numerous behavioral patterns that lead to systematic deviations from rationally optimal behavior. In the context of retirement savings, this can result in substantial pension gaps, and hence in a reduction of the standard of living in the retirement phase. The aim of this work is to introduce a general framework to (simultaneously) assess and evaluate the objectively rational utility and the subjectively perceived attractiveness. We illustrate the approach by means of an application to retirement savings products. Such a combined approach can help to identify or design retirement savings products that create a high (albeit not the maximum possible) objective utility while at the same time being subjectively of high (albeit not maximum possible) attractiveness. We argue that a focus on such products might lead to improved consumer decisions compared to observed decisions that are often driven by subjective attractiveness (resulting in rather low objective utility).

By hedging longevity exposures, annuity providers can reduce both the uncertainty in future cash flows and capital charges in a cost efficient manner. We argue that a separate analysis of these two aspects cannot provide a full picture of the implications of longevity hedging, in particular when using index-based instruments.Hence, we propose a stochastic modeling framework for a joint analysis of the risk-reducing effect and the economic impact of longevity hedges in terms of hedge effectiveness and capital efficiency, respectively. In an economic capital model under Solvency II, a wide selection of customized and index-based instruments is analyzed. We show that different hedging objectives require different instruments on different index populations and discuss the accompanying trade-off between hedge effectiveness and capital efficiency. While customized hedges naturally outperform their index-based counterparts in terms of hedge effectiveness, we show that cost efficient index-based designs may be more capital efficient.

Participating (or with-profit) life insurance contracts play an important role in private old-age provision in many countries. Life insurers pool the assets and liabilities of a heterogeneous portfolio of such contracts and typically perform some return smoothing in the collective investment. Participating contracts were historically equipped with a cliquet-style (year-to-year) guarantee. The current low interest rate environment and regulatory requirements have forced life insurers to develop new product designs with lower and/or different types of guarantees. However, observed demand as well as the findings of several studies show that (year-to-year) guarantees are (subjectively) highly attractive for long-term investors. In this paper, we show that return smoothing alone (that is, without guarantees) can significantly increase the attractiveness for such investors. Most importantly, we show that many (loss averse) long-term investors will even prefer products without guarantee but with smoothed returns over other products with guarantee features. The results hold for long-term investors who not only consider the terminal value but at least partially also evaluate potential annual changes in the account value (even if such changes only have a rather low impact on the decision). Additionally, we show that the descriptive model used in this paper is able to explain the popularity of traditional participating life insurance products in Germany providing further evidence that long-term investors consider potential annual value chances already when making the investment decision.

Purpose The aim of this paper is to modify the shape of utility functions traditionally used in expected utility theory (EUT) to derive optimal retirement saving decisions. Inspired by current reference point based approaches, the authors argue that utility functions with jumps or kinks at certain threshold points might very well be rational. Design/methodology/approach The authors suggest an alternative to typical utility functions used in EUT, to be applied in the context of retirement saving decisions. The authors argue that certain elements that are used to model biases in behavioral models should–in the context of optimal retirement saving decisions–be considered “rational” and hence be included in a normative setting as well. The authors compare the optimal asset allocation derived under such utility functions with results under traditional power utility. Findings The authors find that the considered threshold levels can have a significant impact on the optimal investment decision for some individuals. In particular, the authors show that a much riskier investment than under EUT can become optimal if some level of income is secured by a social security and a significant portion of the distribution of terminal wealth lies below this level. Originality/value Contrary to previous work, this model is especially designed to assess the question of optimal product choice/asset allocation in the specific setting of retirement planning and from a normative point of view. In this regard, the authors first motivate the use of several thresholds and then apply this approach in a capital market model with stochastic stocks and stochastic interest rates to two illustrative investment alternatives.

Increasing life expectancy and thus decreasing mortality rates constitute a global trend that can be observed in almost all countries worldwide. Estimating the current rate at which mortality rates decrease and modeling the future rate of decrease is important for e.g. demographers and actuaries. This task is commonly referred to as mortality trend modeling. In many applications however one needs to carefully distinguish between two different mortality trends: The actual (but unobservable) mortality trend (AMT) prevailing at a certain point in time and the estimated mortality trend (EMT) that an observer would estimate given the (observable) realized mortality up to that point in time. Since the AMT is not observable, an actuary or demographer might misestimate the AMT at any point in time. In particular, he would typically not be able to distinguish between a recent change in the actual trend and a “normal” random fluctuation around the previous long term trend. Depending on the question at hand, the AMT or the EMT or both need to be considered and modeled in analyses. The paper provides a clear definition of and distinction between the actual mortality trend and the estimated mortality trend, discusses their connection, and explains which of the two is relevant for which kind of question. Moreover, a numerically efficient combined model for both trends is specified and calibrated to mortality data. The model component for the actual mortality trend builds on recent findings that mortality appears to evolve log-linear over time with random changes in slope. The model component for the estimated mortality trend is specified such that, given the assumed dynamics for the actual mortality trend, the estimated mortality trend matches the actual trend as close as possible. This provides valuable information on how best estimate mortality assumptions should be derived from the available data in general. Finally, we apply the combined model in practical examples and illustrate the importance of distinguishing between AMT and EMT. We show that, if the AMT is wrongfully assumed observable, the hedge effectiveness of a longevity hedge or the SCR for longevity risk will typically be misestimated significantly.

We use data from a large US life expectancy provider to test for asymmetric information in the secondary life insurance—or life settlements—market. We compare realized lifetimes for a subsample of settled policies relative to all (settled and nonsettled) policies, and find a positive settlement‐survival correlation indicating the existence of informational asymmetry between policyholders and investors. Estimates of the “excess hazard” associated with settling show the effect is temporary and wears off over approximately 8 years. This indicates individuals in our sample possess private information with regards to their near‐term survival prospects and make use of it, which has economic consequences for this market and beyond.

Life-cycle (or target-date) funds are funds, which typically decrease their risk exposure over time. They have been very successful in many countries, particularly in the segment of old age provision. However, Expected Utility Theory (EUT) cannot explain their popularity. Moreover, recent results of Graf (2016), imply that not only EUT but also its behavioral counterpart Cumulative Prospect Theory (CPT) is often not able to explain the popularity of these products, since for each life-cycle fund a corresponding balanced fund can be constructed, which is preferable from the investor's perspective in most circumstances. In a recent paper, Ru ss and Schelling (2018), have argued that potential future changes in an investment's value already impact the decision of long-term investors at outset. Based on this, they have introduced Multi Cumulative Prospect Theory (MCPT), which is based on CPT and considers the subjective utility generated by annual value changes. This paper shows that for MCPT-investors, life-cycle funds are typically more attractive than their corresponding balanced funds since they reduce the potential losses toward the end of the investment horizon. Hence, our findings provide an explanation for inferior decisions in old age provision. This can serve as a basis to improve such decisions.

In economics it has traditionally been assumed that people make all their decisions like the so-called homo oeconomicus - that is, maximizing (expected) utility of total wealth. In recent years, economics increasingly recognized that people often exhibit behavioral patterns which are incompatible with the idea of the homo oeconomicus. The field of behavioral economics incorporates insights from the field of psychology to explain discrepancies between predictions of traditional economic theory and actual observed behavior. In this paper, we summarize a selection of well-established behavioral patterns observed in reality and discuss their relevance for the insurance industry when it comes to better understanding and predicting customer behavior. We also explain that people are not always risk-averse and give a brief overview over Prospect Theory (probably the most popular behavioral economics alternative to Expected Utility Theory), its shortcomings for predicting behavior over a long time horizon, and its extensions. In total, we point out that, since dealing with risks and insurance products requires complex decision making processes, a deep understanding of the impacts of behavioral factors is essential to better assess and explain costumer behavior.

In many countries, traditional participating life insurance (TPLI) contracts are typically equipped with a cliquet-style (year-to-year) guarantee. Life insurers pool the assets and liabilities of a heterogeneous portfolio of TPLI contracts. This allows for intergenerational risk sharing. Together with certain smoothing elements in the collective investment, it also results in rather stable returns for the policyholders. Despite the current low interest rate environment, TPLI contracts are still popular in the segment of retirement savings. Standard approaches which focus solely on the cash-flow at maturity cannot explain their popularity. In a recent paper, Ruß & Schelling (2018) have introduced a descriptive model of decision making which takes into account that potential future changes in the account value impact the decision of long-term investors at outset. Based on this, we illustrate how smoothing and risk sharing elements provided by a life insurer can significantly increase the subjective utility for such investors. Furthermore, we show that for these investors TPLI contracts are more attractive than common unit-linked (guaran∗Institut for Actuarial and Financial Sciences and Ulm University, Lise-Meitner-Str. 14, 89081 Ulm, Germany; Email: j.russ@ifa-ulm.de †Department of Mathematics and Economics, Ulm University, Helmholtzstr. 20, 89081 Ulm, Germany; Email: stefan.schelling@uni-ulm.de (contact author)

A variety of literature addresses the question of how the age distribution of deaths changes over time as life expectancy increases. However, corresponding terms such as extension, compression, or rectangularization are sometimes defined only vaguely, and statistics used to detect certain scenarios can be misleading. The matter is further complicated because mixed scenarios can prevail, and the considered age range can have an impact on observed mortality patterns. In this article, we establish a unique classification framework for realized mortality scenarios that allows for the detection of both pure and mixed scenarios. Our framework determines whether changes of the deaths curve over time show elements of extension or contraction; compression or decompression; left- or right-shifting mortality; and concentration or diffusion. The framework not only can test the presence of a particular scenario but also can assign a unique scenario to any observed mortality evolution. Furthermore, it can detect different mortality scenarios for different age ranges in the same population. We also present a methodology for the implementation of our classification framework and apply it to mortality data for U.S. females.

In diesem Buch wird ein allgemein verständlicher Überblick über ausgewählte Erkenntnisse der modernen Verhaltensökonomie gegeben.