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.

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).

Due to the increasing life expectancy, pension funds, life annuity providers, and reinsurance companies find their longevity risk substantially growing. Correspondingly, various longevity risk-transferring solutions have been developed. Information asymmetry, i.e., general capital market investors have less knowledge of longevity risk than the risk exposure holders and are worried they will be sold a 'lemon', has been a key obstacle to developing a longevity-linked capital market. Using a principal–agent model, we study the optimal transfer of longevity risk between capital market investors and longevity risk exposure holders under information asymmetry. With indemnity longevity swaps as an example, analytical solutions to the optimal incentive-compatible contracts are derived in both a monopolistic and a competitive market setting. We find that information asymmetry could lead to market collapse. However, when the market exists, properly addressing information asymmetry could substantially benefit the market participants.

To mitigate the hedger's longevity risk exposure, this paper proposes a collective longevity swap between a reinsurer (hedge provider) and a group of hedgers (pension plans and annuity providers), and an economic framework to price longevity risk and longevity swaps. Combining the appealing features of two widely discussed longevity swaps, i.e., the indemnity swap and index-based swap, the collective longevity swap requires that reinsurer's payments are based on the longevity risk of the aggregate portfolio of all hedgers, whereas each hedger could receive indemnity payments on their own portfolio. In a general principal-agent pricing model under the incomplete market setting, we determine the optimal risk premiums and hedge rates that maximize the reinsurer's expected profit under a set of the hedgers' participation constraints. We find that, in a competitive market, the proposed collective swap could lead to a higher expected profit for the reinsurer than the indemnity and the index-based swap, and simultaneously improve the benefits of the majority of hedgers without worsening the benefits of the rest. Finally, using a stochastic multi-population mortality model and real-world mortality data, a series of numerical analyses are performed to verify the theoretical findings.

This paper proposes a principal-agent framework to study the optimal transfer of longevity risk between a reinsurer and a hedger under information asymmetry. Most hedgers in the real world have rather small portfolios which are hard to be accurately estimated by the reinsurer. Using indemnity longevity swaps as an example of reinsurance product, we derive the analytical solution to the optimal risk premiums and incentive-compatible hedge demands in a separating equilibrium and examine the conditions for the existence of the separating equilibrium. The theoretical results are evaluated using real-world mortality data.

This paper proposes an innovative retirement product focusing on longevity risk sharing, a contract we refer to as tail index-linked annuity (TILA). Specifically, the proposed TILA pays out variable annual payments, which will be equal to a regular nominal amount when a reference survival index is lower than a predetermined threshold (i.e. normal evolution of longevity risk), and a reduced, index-dependent payment when the threshold is passed (i.e. highly unfavorable evolution of longevity risk). The proposed TILA aims at not only improving the benefits of the policyholders, which has been the focus in recent literature on innovative retirement products, but also reducing the longevity risk exposure of the insurer, particularly for advanced retirement ages. Using real-world mortality data and a stochastic multi-population mortality model, we find that the proposed TILA leads to higher expected lifetime utility than regular annuities for policyholders with different degrees of risk aversions. Meanwhile, numerical analysis shows that the proposed TILA could greatly mitigate the solvency risk of the insurer, leading to a substantially lower loss probability and expected (tail-) loss than regular annuities in the presence of a longevity shock, and therefore could reduce the insurer's required solvency capital under the latest solvency regulations.

We continue to run marathons for fun and for the challenge of our sport. To do so, we train and worry, and plan and hope. We meet new friends and learn ideas that might help us to lower our times. We buy many pairs of shoes, special sox, and other gear. We make elaborate ar- rangements to be away from our families for extended periods of