Special Issue "Life Insurance and Pensions"

A special issue of Risks (ISSN 2227-9091).

Deadline for manuscript submissions: closed (30 November 2015)

Special Issue Editor

Guest Editor
Prof. Dr. Nadine Gatzert

Institute of Insurance Economics and Risk Management, Friedrich-Alexander-University Erlangen-Nürnberg, Lange Gasse 20, D-90403 Nürnberg, Germany
Website | E-Mail
Fax: +0049 911 5302 888
Interests: life insurance mathematics; alternative risk transfer; valuation and management of financial guarantees; enterprise risk management; modeling and management of mortality and longevity risk; regulation and solvency assessment

Special Issue Information

Dear Colleagues,

Against the background of demographic development and changing consumer needs, innovations in life insurance and pension have become of increasing relevance in the insurance industry in virtually all industrialized countries. This will be even more apparent in the future, a development also due to the serious problems of social security systems. At the same time, insurers face increasing challenges in regard to low interest rates, volatile capital markets, longevity and mortality risk, an increasing cost pressure, as well as new insurance regulations such as Solvency II. The aim of this Special Issue is to highlight these developments and successful responses in regard to products and risk and capital management in life insurance and pension, where contributions can be related, but are not limited to the following areas:

• Innovations in life insurance and pension against the background of new regulatory requirements, longevity risk, and low interest rates
• The future of guarantees in life and pension products
• Policyholder behavior regarding options and guarantees embedded in life and pension products
• Enhanced annuities
• Solvency regulation
• The impact of Solvency II on life insurers’ risk and capital management
• Solvency risk measures with application to life insurance
• Challenges and new approaches in risk and capital management in life insurance and pension
• Reinsurance solutions and the securitization of longevity and mortality risks
• Evaluating life insurance and pension products from the insurer’s and the customer’s perspective
• Modeling and managing biometric risk in life insurance and pension products
• The role of the life insurance and pension industry in the economy
• Sustainable social security systems and government-subsidized pension schemes
• Empirical studies on life insurance and pension

Prof. Dr. Nadine Gatzert
Guest Editor

Manuscript Submission Information

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Keywords

  • innovation
  • life insurance
  • pension
  • guarantee
  • policyholder behavior
  • enhanced annuities
  • solvency regulation

Published Papers (9 papers)

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Research

Open AccessArticle A Unified Pricing of Variable Annuity Guarantees under the Optimal Stochastic Control Framework
Risks 2016, 4(3), 22; doi:10.3390/risks4030022
Received: 4 February 2016 / Revised: 25 May 2016 / Accepted: 25 June 2016 / Published: 5 July 2016
Cited by 2 | PDF Full-text (735 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we review pricing of the variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal
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In this paper, we review pricing of the variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework and review the existing numerical methods. We also discuss pricing under the complete/incomplete financial market models, stochastic mortality and optimal/sub-optimal policyholder behavior, and in the presence of taxes. For numerical valuation of these contracts in the case of simple risky asset process, we develop a direct integration method based on the Gauss-Hermite quadratures with a one-dimensional cubic spline for calculation of the expected contract value, and a bi-cubic spline interpolation for applying the jump conditions across the contract cashflow event times. This method is easier to implement and faster when compared to the partial differential equation methods if the transition density (or its moments) of the risky asset underlying the contract is known in closed form between the event times. We present accurate numerical results for pricing of a Guaranteed Minimum Accumulation Benefit (GMAB) guarantee available on the market that can serve as a numerical benchmark for practitioners and researchers developing pricing of variable annuity guarantees to assess the accuracy of their numerical implementation. Full article
(This article belongs to the Special Issue Life Insurance and Pensions)
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Open AccessArticle Spouses’ Dependence across Generations and Pricing Impact on Reversionary Annuities
Risks 2016, 4(2), 16; doi:10.3390/risks4020016
Received: 21 October 2015 / Revised: 2 May 2016 / Accepted: 4 May 2016 / Published: 25 May 2016
Cited by 1 | PDF Full-text (396 KB) | HTML Full-text | XML Full-text
Abstract
This paper studies the dependence between coupled lives, i.e., the spouses’ dependence, across different generations, and its effects on prices of reversionary annuities in the presence of longevity risk. Longevity risk is represented via a stochastic mortality intensity. We find that a
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This paper studies the dependence between coupled lives, i.e., the spouses’ dependence, across different generations, and its effects on prices of reversionary annuities in the presence of longevity risk. Longevity risk is represented via a stochastic mortality intensity. We find that a generation-based model is important, since spouses’ dependence decreases when passing from older generations to younger generations. The independence assumption produces quantifiable mispricing of reversionary annuities, with different effects on different generations. The research is conducted using a well-known dataset of double life contracts. Full article
(This article belongs to the Special Issue Life Insurance and Pensions)
Open AccessFeature PaperArticle Participating Life Insurance Products with Alternative Guarantees: Reconciling Policyholders’ and Insurers’ Interests
Risks 2016, 4(2), 11; doi:10.3390/risks4020011
Received: 26 November 2015 / Revised: 18 April 2016 / Accepted: 25 April 2016 / Published: 5 May 2016
Cited by 2 | PDF Full-text (2650 KB) | HTML Full-text | XML Full-text
Abstract
Traditional participating life insurance contracts with year-to-year (cliquet-style) guarantees have come under pressure in the current situation of low interest rates and volatile capital markets, in particular when priced in a market-consistent valuation framework. In addition, such guarantees lead to rather high capital
[...] Read more.
Traditional participating life insurance contracts with year-to-year (cliquet-style) guarantees have come under pressure in the current situation of low interest rates and volatile capital markets, in particular when priced in a market-consistent valuation framework. In addition, such guarantees lead to rather high capital requirements under risk-based solvency frameworks such as Solvency II or the Swiss Solvency Test (SST). Therefore, insurers in several countries have developed new forms of participating products with alternative (typically weaker and/or lower) guarantees that are less risky for the insurer. In a previous paper, it has been shown that such alternative product designs can lead to higher capital efficiency, i.e., higher and more stable profits and reduced capital requirements. As a result, the financial risk for the insurer is significantly reduced while the main guarantee features perceived and requested by the policyholder are preserved. Based on these findings, this paper now combines the insurer’s and the policyholder’s perspective by analyzing product versions that compensate policyholders for the less valuable guarantees. We particularly identify combinations of asset allocation and profit participation rate for the different product designs that lead to an identical expected profit for the insurer (and identical risk-neutral value for the policyholder), but differ with respect to the insurer’s risk and solvency capital requirements as well as with respect to the real-world return distribution for the policyholder. We show that alternative products can be designed in a way that the insurer’s expected profitability remains unchanged, the insurer’s risk and hence capital requirement is substantially reduced and the policyholder’s expected return is increased. This illustrates that such products might be able to reconcile insurers’ and policyholders’ interests and serve as an alternative to the rather risky cliquet-style products. Full article
(This article belongs to the Special Issue Life Insurance and Pensions)
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Open AccessArticle Premiums for Long-Term Care Insurance Packages: Sensitivity with Respect to Biometric Assumptions
Risks 2016, 4(1), 3; doi:10.3390/risks4010003
Received: 19 November 2015 / Accepted: 2 February 2016 / Published: 22 February 2016
Cited by 1 | PDF Full-text (344 KB) | HTML Full-text | XML Full-text
Abstract
Long-term care insurance (LTCI) covers are rather recent products, in the framework of health insurance. It follows that specific biometric data are scanty; pricing and reserving problems then arise because of difficulties in the choice of appropriate technical bases. Different benefit structures imply
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Long-term care insurance (LTCI) covers are rather recent products, in the framework of health insurance. It follows that specific biometric data are scanty; pricing and reserving problems then arise because of difficulties in the choice of appropriate technical bases. Different benefit structures imply different sensitivity degrees with respect to changes in biometric assumptions. Hence, an accurate sensitivity analysis can help in designing LTCI products and, in particular, in comparing stand-alone products to combined products, i.e., packages including LTCI benefits and other lifetime-related benefits. Numerical examples show, in particular, that the stand-alone cover is much riskier than all of the LTCI combined products that we have considered. As a consequence, the LTCI stand-alone cover is a highly “absorbing” product as regards capital requirements for solvency purposes. Full article
(This article belongs to the Special Issue Life Insurance and Pensions)
Open AccessArticle The Impact of Guarantees on the Performance of Pension Saving Schemes: Insights from the Literature
Risks 2015, 3(4), 515-542; doi:10.3390/risks3040515
Received: 13 July 2015 / Accepted: 16 November 2015 / Published: 20 November 2015
Cited by 1 | PDF Full-text (620 KB) | HTML Full-text | XML Full-text
Abstract
Guarantees are often seen as the key characteristics of pension saving products, but securing them can become costly and is of central relevance especially in the course of the current low interest rate environment. In this article, we deal with the question of
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Guarantees are often seen as the key characteristics of pension saving products, but securing them can become costly and is of central relevance especially in the course of the current low interest rate environment. In this article, we deal with the question of how costly the typical types of guarantees are, in the sense that they reduce a pension saving scheme’s financial performance over time. In this context, we aim to provide a presentation of insights from selected literature studying the impact of point-to-point guarantees and cliquet-style interest rate guarantees on the performance of pension contracts. The comparative analysis emphasizes that, in most cases, guarantee costs are not negligible with regard to a contract’s financial performance, especially compared to benchmarks, and that customers knowingly opt for such guarantees (or not) is, thus, indispensable. To further investigate the willingness-to-pay for guarantees in life insurance is an area for future research, in particular for innovative contract design. Full article
(This article belongs to the Special Issue Life Insurance and Pensions)
Open AccessArticle Life Insurance Cash Flows with Policyholder Behavior
Risks 2015, 3(3), 290-317; doi:10.3390/risks3030290
Received: 16 March 2015 / Accepted: 5 July 2015 / Published: 24 July 2015
Cited by 1 | PDF Full-text (310 KB) | HTML Full-text | XML Full-text
Abstract
The problem of the valuation of life insurance payments with policyholder behavior is studied. First, a simple survival model is considered, and it is shown how cash flows without policyholder behavior can be modified to include surrender and free policy behavior by calculation
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The problem of the valuation of life insurance payments with policyholder behavior is studied. First, a simple survival model is considered, and it is shown how cash flows without policyholder behavior can be modified to include surrender and free policy behavior by calculation of simple integrals. In the second part, a more general disability model with recovery is studied. Here, cash flows are determined by solving a modified Kolmogorov forward differential equation. We conclude the paper with numerical examples illustrating the methods proposed and the impact of policyholder behavior. Full article
(This article belongs to the Special Issue Life Insurance and Pensions)
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Open AccessArticle A Two-Account Life Insurance Model for Scenario-Based Valuation Including Event Risk
Risks 2015, 3(2), 183-218; doi:10.3390/risks3020183
Received: 30 November 2014 / Accepted: 27 May 2015 / Published: 4 June 2015
Cited by 2 | PDF Full-text (613 KB) | HTML Full-text | XML Full-text
Abstract
Using a two-account model with event risk, we model life insurance contracts taking into account both guaranteed and non-guaranteed payments in participating life insurance as well as in unit-linked insurance. Here, event risk is used as a generic term for life insurance events,
[...] Read more.
Using a two-account model with event risk, we model life insurance contracts taking into account both guaranteed and non-guaranteed payments in participating life insurance as well as in unit-linked insurance. Here, event risk is used as a generic term for life insurance events, such as death, disability, etc. In our treatment of participating life insurance, we have special focus on the bonus schemes “consolidation” and “additional benefits”, and one goal is to formalize how these work and interact. Another goal is to describe similarities and differences between participating life insurance and unit-linked insurance. By use of a two-account model, we are able to illustrate general concepts without making the model too abstract. To allow for complicated financial markets without dramatically increasing the mathematical complexity, we focus on economic scenarios. We illustrate the use of our model by conducting scenario analysis based on Monte Carlo simulation, but the model applies to scenarios in general and to worst-case and best-estimate scenarios in particular. In addition to easy computations, our model offers a common framework for the valuation of life insurance payments across product types. This enables comparison of participating life insurance products and unit-linked insurance products, thus building a bridge between the two different ways of formalizing life insurance products. Finally, our model distinguishes itself from the existing literature by taking into account the Markov model for the state of the policyholder and, hereby, facilitating event risk. Full article
(This article belongs to the Special Issue Life Insurance and Pensions)
Open AccessArticle Portability, Salary and Asset Price Risk: A Continuous-Time Expected Utility Comparison of DB and DC Pension Plans
Risks 2015, 3(1), 77-102; doi:10.3390/risks3010077
Received: 29 November 2014 / Accepted: 5 March 2015 / Published: 13 March 2015
Cited by 1 | PDF Full-text (330 KB) | HTML Full-text | XML Full-text
Abstract
This paper compares two different types of private retirement plans from the perspective of a representative beneficiary: a defined benefit (DB) and a defined contribution (DC) plan. While salary risk is the main common risk factor in DB and DC pension plans, one
[...] Read more.
This paper compares two different types of private retirement plans from the perspective of a representative beneficiary: a defined benefit (DB) and a defined contribution (DC) plan. While salary risk is the main common risk factor in DB and DC pension plans, one of the key differences is that DB plans carry portability risks, whereas DC plans bear asset price risk. We model these tradeoffs explicitly in this paper and compare these two plans in a utility-based framework. Our numerical analysis focuses on answering the question of when the beneficiary is indifferent between the DB and DC plan. Most of our results confirm the findings in the existing literature, among which, e.g., portability losses considerably reduce the relative attractiveness of the DB plan. However, we also find that the attractiveness of the DB plan can decrease in the level of risk aversion, which is inconsistent with the existing literature. Full article
(This article belongs to the Special Issue Life Insurance and Pensions)
Open AccessArticle Safety Margins for Systematic Biometric and Financial Risk in a Semi-Markov Life Insurance Framework
Risks 2015, 3(1), 35-60; doi:10.3390/risks3010035
Received: 9 November 2014 / Accepted: 8 January 2015 / Published: 19 January 2015
PDF Full-text (1325 KB) | HTML Full-text | XML Full-text
Abstract
Insurance companies use conservative first order valuation bases to calculate insurance premiums and reserves. These valuation bases have a significant impact on the insurer’s solvency and on the premiums of the insurance products. Safety margins for systematic biometric and financial risk are in
[...] Read more.
Insurance companies use conservative first order valuation bases to calculate insurance premiums and reserves. These valuation bases have a significant impact on the insurer’s solvency and on the premiums of the insurance products. Safety margins for systematic biometric and financial risk are in practice typically chosen as time-constant percentages on top of the best estimate transition intensities. We develop a risk-oriented method for the allocation of a total safety margin to the single safety margins at each point in time and each state. In a case study, we demonstrate the suitability of the proposed method in different frameworks. The results show that the traditional method yields an unwanted variability of the safety level with respect to time, whereas the variability can be significantly reduced by the new method. Furthermore, the case study supports the German 60 percent rule for the technical interest rate. Full article
(This article belongs to the Special Issue Life Insurance and Pensions)
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