Editorial

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Open AccessEditorial

Special Issue “Actuarial and Financial Risks in Life Insurance, Pensions and Household Finance”

by Luca Regis

Risks 2017, 5(4), 63; https://doi.org/10.3390/risks5040063 - 05 Dec 2017

Cited by 1 | Viewed by 2579

The aim of the Special Issue is to address some of the main challenges individuals and companies face in managing financial and actuarial risks, when dealing with their investment/retirement or business-related decisions [...] Full article

(This article belongs to the Special Issue Actuarial and Financial Risks in Life Insurance, Pensions and Household Finance)

Research

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Open AccessArticle

Backtesting the Lee–Carter and the Cairns–Blake–Dowd Stochastic Mortality Models on Italian Death Rates

by Carlo Maccheroni and Samuel Nocito

Risks 2017, 5(3), 34; https://doi.org/10.3390/risks5030034 - 04 Jul 2017

Cited by 10 | Viewed by 6273

Abstract

This work proposes a backtesting analysis that compares the Lee–Carter and the Cairns–Blake–Dowd mortality models, employing Italian data. The mortality data come from the Italian National Statistics Institute (ISTAT) database and span the period 1975–2014, over which we computed back-projections evaluating the performances [...] Read more.

This work proposes a backtesting analysis that compares the Lee–Carter and the Cairns–Blake–Dowd mortality models, employing Italian data. The mortality data come from the Italian National Statistics Institute (ISTAT) database and span the period 1975–2014, over which we computed back-projections evaluating the performances of the models compared with real data. We propose three different backtest approaches, evaluating the goodness of short-run forecast versus medium-length ones. We find that neither model was able to capture the improving shock on mortality observed for the male population on the analysed period. Moreover, the results suggest that CBD forecasts are reliable prevalently for ages above 75, and that LC forecasts are basically more accurate for this data. Full article

(This article belongs to the Special Issue Actuarial and Financial Risks in Life Insurance, Pensions and Household Finance)

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Applying spectral biclustering to mortality data

by Gabriella Piscopo and Marina Resta

Risks 2017, 5(2), 24; https://doi.org/10.3390/risks5020024 - 04 Apr 2017

Cited by 6 | Viewed by 4273

Abstract

We apply spectral biclustering to mortality datasets in order to capture three relevant aspects: the period, the age and the cohort effects, as their knowledge is a key factor in understanding actuarial liabilities of private life insurance companies, pension funds as well as [...] Read more.

We apply spectral biclustering to mortality datasets in order to capture three relevant aspects: the period, the age and the cohort effects, as their knowledge is a key factor in understanding actuarial liabilities of private life insurance companies, pension funds as well as national pension systems. While standard techniques generally fail to capture the cohort effect, on the contrary, biclustering methods seem particularly suitable for this aim. We run an exploratory analysis on the mortality data of Italy, with ages representing genes, and years as conditions: by comparison between conventional hierarchical clustering and spectral biclustering, we observe that the latter offers more meaningful results. Full article

(This article belongs to the Special Issue Actuarial and Financial Risks in Life Insurance, Pensions and Household Finance)

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Mathematical Analysis of Replication by Cash Flow Matching

by Jan Natolski and Ralf Werner

Risks 2017, 5(1), 13; https://doi.org/10.3390/risks5010013 - 28 Feb 2017

Cited by 6 | Viewed by 6063

Abstract

The replicating portfolio approach is a well-established approach carried out by many life insurance companies within their Solvency II framework for the computation of risk capital. In this note,weelaborateononespeciﬁcformulationofareplicatingportfolioproblem. Incontrasttothetwo most popular replication approaches, it does not yield an analytic solution (if, at [...] Read more.

The replicating portfolio approach is a well-established approach carried out by many life insurance companies within their Solvency II framework for the computation of risk capital. In this note,weelaborateononespeciﬁcformulationofareplicatingportfolioproblem. Incontrasttothetwo most popular replication approaches, it does not yield an analytic solution (if, at all, a solution exists andisunique). Further,althoughconvex,theobjectivefunctionseemstobenon-smooth,andhencea numericalsolutionmightthusbemuchmoredemandingthanforthetwomostpopularformulations. Especially for the second reason, this formulation did not (yet) receive much attention in practical applications, in contrast to the other two formulations. In the following, we will demonstrate that the (potential) non-smoothness can be avoided due to an equivalent reformulation as a linear second order cone program (SOCP). This allows for a numerical solution by efﬁcient second order methods like interior point methods or similar. We also show that—under weak assumptions—existence and uniqueness of the optimal solution can be guaranteed. We additionally prove that—under a further similarly weak condition—the fair value of the replicating portfolio equals the fair value of liabilities. Based on these insights, we argue that this unloved stepmother child within the replication problem family indeed represents an equally good formulation for practical purposes. Full article

(This article belongs to the Special Issue Actuarial and Financial Risks in Life Insurance, Pensions and Household Finance)

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A Discussion of a Risk-Sharing Pension Plan

by Catherine Donnelly

Risks 2017, 5(1), 12; https://doi.org/10.3390/risks5010012 - 14 Feb 2017

Cited by 3 | Viewed by 5349

Abstract

I show that risk-sharing pension plans can reduce some of the shortcomings of defined benefit and defined contributions plans. The risk-sharing pension plan presented aims to improve the stability of benefits paid to generations of members, while allowing them to enjoy the expected [...] Read more.

I show that risk-sharing pension plans can reduce some of the shortcomings of defined benefit and defined contributions plans. The risk-sharing pension plan presented aims to improve the stability of benefits paid to generations of members, while allowing them to enjoy the expected advantages of a risky investment strategy. The plan does this by adjusting the investment strategy and benefits in response to a changing funding level, motivated by the with-profits contract proposed by Goecke (2013). He suggests a mean-reverting log reserve (or funding) ratio, where mean reversion occurs through adjustments to the investment strategy and declared bonuses. To measure the robustness of the plan to human factors, I introduce a measurement of disappointment, where disappointment is high when there are many consecutive years over which benefit payments are declining. Another measure introduced is devastation, where devastation occurs when benefit payments are zero. The motivation is that members of a pension plan who are easily disappointed or likely to get no benefit, are more likely to exit the plan. I find that the risk-sharing plan offers more disappointment than a defined contribution plan, but it eliminates the devastation possible in a plan that tries to accumulate contributions at a steadily increasing rate. The proposed risk-sharing plan can give a narrower range of benefits than in a defined contribution plan. Thus it can offer a stable benefit to members without the risk of running out of money. Full article

(This article belongs to the Special Issue Actuarial and Financial Risks in Life Insurance, Pensions and Household Finance)

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The Shifting Shape of Risk: Endogenous Market Failure for Insurance

by Thomas G. Koch

Risks 2017, 5(1), 9; https://doi.org/10.3390/risks5010009 - 27 Jan 2017

Cited by 1 | Viewed by 6003

Abstract

This article considers an economy where risk is insurable, but selection determines the pool of individuals who take it up. First, we demonstrate that the comparative statics of these economies do not necessarily depend on its marginal selection (adverse versus favorable), but rather [...] Read more.

This article considers an economy where risk is insurable, but selection determines the pool of individuals who take it up. First, we demonstrate that the comparative statics of these economies do not necessarily depend on its marginal selection (adverse versus favorable), but rather other characteristics. We then use repeated cross-sections of medical expenditures in the U.S. to understand the role of changes in the medical risk distribution on the fraction of Americans without medical insurance. We ﬁnd that both the level and the shape of the distribution of risk are important in determining the equilibrium quantity of insurance. Symmetric changes in risk (e.g., shifts in the price of medical care) better explain the shifting insurance rate over time. Asymmetric changes (e.g., associated with a shifting age distribution) are not as important. Full article

(This article belongs to the Special Issue Actuarial and Financial Risks in Life Insurance, Pensions and Household Finance)

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Minimum Protection in DC Funding Pension Plans and Margrabe Options

by Pierre Devolder and Sébastien De Valeriola

Risks 2017, 5(1), 5; https://doi.org/10.3390/risks5010005 - 18 Jan 2017

Cited by 5 | Viewed by 4706

Abstract

The regulation on the Belgian occupational pension schemes has been recently changed. The new law allows for employers to choose between two different types of guarantees to offer to their affiliates. In this paper, we address the question arising naturally: which of the [...] Read more.

The regulation on the Belgian occupational pension schemes has been recently changed. The new law allows for employers to choose between two different types of guarantees to offer to their affiliates. In this paper, we address the question arising naturally: which of the two guarantees is the best one? In order to answer that question, we set up a stochastic model and use financial pricing tools to compare the methods. More specifically, we link the pension liabilities to a portfolio of financial assets and compute the price of exchange options through the Margrabe formula. Full article

(This article belongs to the Special Issue Actuarial and Financial Risks in Life Insurance, Pensions and Household Finance)

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Open AccessFeature PaperArticle

The Effects of Largest Claim and Excess of Loss Reinsurance on a Company’s Ruin Time and Valuation

by Yuguang Fan, Philip S. Griffin, Ross Maller, Alexander Szimayer and Tiandong Wang

Risks 2017, 5(1), 3; https://doi.org/10.3390/risks5010003 - 06 Jan 2017

Cited by 5 | Viewed by 7763

Abstract

We compare two types of reinsurance: excess of loss (EOL) and largest claim reinsurance (LCR), each of which transfers the payment of part, or all, of one or more large claims from the primary insurance company (the cedant) to a reinsurer. The primary [...] Read more.

We compare two types of reinsurance: excess of loss (EOL) and largest claim reinsurance (LCR), each of which transfers the payment of part, or all, of one or more large claims from the primary insurance company (the cedant) to a reinsurer. The primary insurer’s point of view is documented in terms of assessment of risk and payment of reinsurance premium. A utility indifference rationale based on the expected future dividend stream is used to value the company with and without reinsurance. Assuming the classical compound Poisson risk model with choices of claim size distributions (classified as heavy, medium and light-tailed cases), simulations are used to illustrate the impact of the EOL and LCR treaties on the company’s ruin probability, ruin time and value as determined by the dividend discounting model. We find that LCR is at least as effective as EOL in averting ruin in comparable finite time horizon settings. In instances where the ruin probability for LCR is smaller than for EOL, the dividend discount model shows that the cedant is able to pay a larger portion of the dividend for LCR reinsurance than for EOL while still maintaining company value. Both methods reduce risk considerably as compared with no reinsurance, in a variety of situations, as measured by the standard deviation of the company value. A further interesting finding is that heaviness of tails alone is not necessarily the decisive factor in the possible ruin of a company; small and moderate sized claims can also play a significant role in this. Full article

(This article belongs to the Special Issue Actuarial and Financial Risks in Life Insurance, Pensions and Household Finance)

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Open AccessFeature PaperArticle

Compositions of Conditional Risk Measures and Solvency Capital

by Pierre Devolder and Adrien Lebègue

Risks 2016, 4(4), 49; https://doi.org/10.3390/risks4040049 - 16 Dec 2016

Cited by 1 | Viewed by 5347

Abstract

In this paper, we consider compositions of conditional risk measures in order to obtain time-consistent dynamic risk measures and determine the solvency capital of a life insurer selling pension liabilities or a pension fund with a single cash-flow at maturity. We first recall [...] Read more.

In this paper, we consider compositions of conditional risk measures in order to obtain time-consistent dynamic risk measures and determine the solvency capital of a life insurer selling pension liabilities or a pension fund with a single cash-flow at maturity. We first recall the notion of conditional, dynamic and time-consistent risk measures. We link the latter with its iterated property, which gives us a way to construct time-consistent dynamic risk measures from a backward iteration scheme with the composition of conditional risk measures. We then consider particular cases with the conditional version of the value at risk, tail value at risk and conditional expectation measures. We finally give an application of these measures with the determination of the solvency capital of a pension liability, which offers a fixed guaranteed rate without any intermediate cash-flow. We assume that the company is fully hedged against the mortality and underwriting risks. Full article

(This article belongs to the Special Issue Actuarial and Financial Risks in Life Insurance, Pensions and Household Finance)

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The Myth of Methuselah and the Uncertainty of Death: The Mortality Fan Charts

by Kevin Dowd, David Blake and Andrew J. G. Cairns

Risks 2016, 4(3), 21; https://doi.org/10.3390/risks4030021 - 04 Jul 2016

Cited by 4 | Viewed by 7056

Abstract

This paper uses mortality fan charts to illustrate prospective future male mortality. These fan charts show both the most likely path of male mortality and the bands of uncertainty surrounding that path. The fan charts are based on a model of male mortality [...] Read more.

This paper uses mortality fan charts to illustrate prospective future male mortality. These fan charts show both the most likely path of male mortality and the bands of uncertainty surrounding that path. The fan charts are based on a model of male mortality that is known to provide a good fit to UK mortality data. The fan charts suggest that there are clear limits to longevity—that future mortality rates are very uncertain and tend to become more uncertain the further ahead the forecast—and that forecasts of future mortality uncertainty must also take account of uncertainty in the parameters of the underlying mortality model. Full article

(This article belongs to the Special Issue Actuarial and Financial Risks in Life Insurance, Pensions and Household Finance)

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