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European Actuarial Journal
Erschienen in: European Actuarial Journal 2/2018

01.09.2018 | Original Research Paper

Policy characteristics and stakeholder returns in participating life insurance: which contracts can lead to a win-win?

verfasst von: Charbel Mirza, Joël Wagner

Erschienen in: European Actuarial Journal | Ausgabe 2/2018

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Abstract

Participating life insurance contracts and pension plans often include a return guarantee and participation in the surplus of the institution’s result. The final account value in such contracts depends on the investment policy driven by solvency requirements, as well as on the level of market returns, the guarantee and the participation rates. Using a contingent claim model for such contracts, we assume a competitive market with minimum solvency requirements similar to Solvency II. We consider solvency requirements on maturity and 1-year time horizons, as well as contracts with single and periodic premium payments. Through numerical analyses, we link the expected returns for equity holders and policyholders in various situations. Using the return on equity and policyholder internal rate of return along with utility measures, we assess which contract settings optimize the return compromise for both stakeholders in a low-interest-rate environment. Our results extend the academic literature by building on the work by Schmeiser and Wagner (J Risk Insur 82(3):659–686, 2015) and are relevant for practitioners, given the current financial market environment and difficulties in insurance-linked savings plans with guarantees.
Vorheriger Artikel The impact of longevity and investment risk on a portfolio of life insurance liabilities
Nächster Artikel Old-age care prevalence in Switzerland: drivers and future development

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Fußnoten
1
In this paper, we focus on the products offered in Switzerland and Germany, where participating life insurance with guarantees is very popular. In Swiss collective life insurance contracts, the interest rate defined by the authorities is to be followed exactly. The lower bound for policyholders’ profit participation holds in German participating life insurance contracts and in Swiss collective life insurance.
 
2
A short review of insurer defaults linked to interest rate guarantees is provided, for example, in the Introduction in Schmeiser and Wagner [30]. The references cited therein (see their Footnote 2) give more detailed information. Following the introduction of the Solvency II regulation in the European Union, some of the conditions, in particular those linked to the asset allocation have been relaxed and replaced by a more comprehensive risk assessment, see, e.g., Braun et al. [4].
 
3
In this simple setup, following Schmeiser and Wagner [30], we directly link the investment return to the return credited to the policyholder account. Since in practice smoothing mechanisms for the surplus distribution are in place, our results overestimate the asset volatility. We show that our conceptual findings remain valid by comparing our results with simulations using a much lower asset volatility (compare the results from Tables 4 and 5 in Sect. 4.1 with Tables 8 and 9 reported in the Appendix).
 
4
We do not consider that a guarantee fund will step in and ensure the interest g, see, e.g. [28, 29].
 
5
With this consideration, we importantly differentiate our reference setting from Schmeiser and Wagner [30], where a ruin probability of 0.5% is considered for the 10-year contract case.
 
6
Given that we used continuous compounding for \(r_\mathrm{f}\) and discrete compounding for g (see Eqs. 3, 5), \(r_\mathrm{f}=1.0\%\) does not correspond to the limit point for \(g=1.0\%\). In fact, \(r_\mathrm{f}\) could decrease to \(\log (1+g)\approx 0.995\%\).
 
7
In their paper, Braun et al. [3] analyze in detail the level of guaranteed interest rate to choose to optimize the policyholders’ utility while keeping the insurance product more valuable than a simple direct investment. The comparison of the utility from insurance contracts and from other investment forms has also been the focus of Schmeiser and Wagner [30, 31]. In this latter study, transaction costs are also taken into account.
 
8
For the evaluation under the \(\mathbb {Q}\)-measure, \(\mu _\mathrm{B}\) is replaced by \(r_\mathrm{f}\) in Eq. (4), defining \(R_t^\mathbb {Q}\).
 
9
The inequality holds because the policy is solvent at time \(t-1\), i.e., \(A_{t-1}>P_{t-1}\), and the premium \(\Pi _{t-1}>0\).
 
10
In fact for \(\frac{g}{\alpha }<\frac{1+g}{\theta _{t-1}}-1\) we have \( \text {Pr}\left[ R_t^\mathbb {P}<\left( \frac{1+g}{\theta _{t-1}}-1\right) ;\,R_{t}^\mathbb {P}<\frac{g}{\alpha }\right] =\text {Pr}\left( R_{t}^\mathbb {P}<\frac{g}{\alpha }\right) \) and we rewrite \(g/\alpha<\frac{1+g}{\theta _{t-1}}-1\iff \theta _{t-1}<\frac{1+g}{1+g/\alpha }=\theta ^*\) where we need \((1+g/\alpha )>0\). In our application with \(\alpha \) close to 100% and g close to zero this condition is fulfilled.
 
11
In the case where \(\frac{g}{\alpha }>\frac{1+g}{\theta _{t-1}}-1\) we have \(\text {Pr}\left( \frac{g}{\alpha }<R_t^\mathbb {P}<\frac{1-\theta _{t-1}}{\theta _{t-1}-\alpha }\right) =0\) and \(\text {Pr}\left[ R_t^\mathbb {P}<\left( \frac{1+g}{\theta _{t-1}}-1\right) ;R_{t}^\mathbb {P}<\frac{g}{\alpha }\right] =\text {Pr}\left( R_{t}^\mathbb {P}<\frac{1+g}{\theta _{t-1}}-1\right) \).
 
Literatur
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Metadaten
Titel
Policy characteristics and stakeholder returns in participating life insurance: which contracts can lead to a win-win?
verfasst von
Charbel Mirza
Joël Wagner
Publikationsdatum
01.09.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
European Actuarial Journal / Ausgabe 2/2018
Print ISSN: 2190-9733
Elektronische ISSN: 2190-9741
DOI
https://doi.org/10.1007/s13385-018-0179-1

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