In this paper, we study a continuous-time bivariate risk process in which each individual line of business implements a dividend barrier strategy. The insurance portfolios of the two insurers are correlated as they are subject to common shocks that induce dependent claims. To analyse the expected discounted dividends until the joint ruin time of the bivariate process (i.e. exit from the positive quadrant), we propose a discrete-time counterpart of the model and apply a bivariate extension of the Dickson−Waters discretisation with the use of a bivariate Panjer-type recursion. Detailed numerical examples under different dependencies via common shocks, copulas and proportional reinsurance are discussed, and applications to optimal problems in reinsurance, capital allocation and dividends are given. It is also illustrated that the optimal pair of dividend barriers maximising the dividend function is dependent on the initial surplus levels. A modified type of dividend barrier strategy is proposed towards the end.

Non-homogeneous renewal processes are not yet well established. One of the tools necessary for studying these processes is the non-homogeneous time convolution. Renewal theory has great relevance in general in economics and in particular in actuarial science, however, most actuarial problems are connected with the age of the insured person. The introduction of non-homogeneity in the renewal processes brings actuarial applications closer to the real world. This paper will define the non-homogeneous time convolutions and try to give order to the non-homogeneous renewal processes. The numerical aspects of these processes are then dealt with and a real data application to an aspect of motorcar insurance is proposed.

Human longevity is changing, but at what rate? Insurance claims are increasing, but at what rate? Are the trends that we glean from data true or illusionary? The shocking fact is that true trends might be quite different from those that we actually see from visualised data. Indeed, in some situations the upward trends (e.g. inflation) may even look decreasing (e.g. deflation). In this paper, we discuss this “trends in disguise” phenomenon in detail and offer a way for estimating true trends.

This paper is a continuation of and a supplement to the paper by Jørgensen & Linnemann. Both papers deal with TimePension – a (formula-based) smoothed investment-linked annuity pension scheme. Both papers compare TimePension with other pension savings products using stochastic financial simulation. TimePension as well as the financial model and simulation concept being used in both papers were introduced in the paper op cit.

Jørgensen & Linnemann compare TimePension with a traditional with-profits scheme involving bonus entitlement and an investment-linked Unit Link scheme with a fixed proportion of assets invested in equities and other so-called risky assets. Here, TimePension is compared with two investment-linked life-cycle (target date) products. The focus is especially on the decumulation period, and we show that despite the fact that the life-cycle products reduce investment risk in retirement (compared with TimePension’s fixed proportional allocation of assets), the year-over-year stability in benefits provided by TimePension cannot be matched. Even though the overall investment risk on accumulated benefits is at the same level, TimePension provide year-over-year stability, also in case of sharp price changes in the financial market.

Our results show that not only investment profiles define the stability of annuity benefits over time. In addition, more fundamental elements of the product design are important. The perspective on product design and development is Danish, but two of the compared products are generic life-cycle products that exist in equivalent forms in many countries. Similarly, the smoothed income annuities could also become an alternative product design in an international perspective.

Home equity release products have been promoted as a potential solution to residential long-term care costs for the elderly. Lower than expected utilisation of home equity release loans has prompted efforts to better model and price the no-negative-equity-guarantee (NNEG) built into the contracts, but loan rates are still widely perceived by homeowners as being unattractive. We propose the introduction of a new adjustable rate loan based on a regional house price index, with the NNEG being borne by a specially created intermediary. The proposed approach allows us to directly address and separately price the basis risk between individual house price returns and index returns. In addition, it offers the opportunity to create securities based on residential real estate that would be attractive to a wider class of investors. The alternative risk-sharing mechanism creates a more transparent and simple pricing structure for the loans. We then use house sales data to demonstrate the approach. We find in our sample that it would be possible to make higher loans than seen in previous literature using standard roll-up contracts. In the most favourable scenario for our simulations, the maximum loan is 89% of the appraised home value if the loan is advanced as a lump sum and 95% if the loan is advanced in instalments.

In this paper we calculate and compare diagnosis and net premium rates for critical illness insurance using different models for the claim delay distribution (CDD). The choice of CDD affects the diagnosis rates and hence the net premium rates in two ways: through the estimation of missing dates of diagnosis and through the adjustment of the exposure to allow for claims diagnosed but not settled in the observation period. We consider two CDDs: a three-parameter Burr distribution and a lognormal distribution. Our conclusion, based on a single, but extensive, data set, is that net premium rates are not significantly affected by the choice of CDD.

With the advent of formal regulatory requirements for rigorous risk-based, or economic, capital quantification for the financial risk management of banking and insurance sectors, regulators and policy-makers are turning their attention to the pension sector, the other integral player in the financial markets. In this paper, we analyse the impact of applying economic capital techniques to defined benefit pension schemes in the United Kingdom. We propose two alternative economic capital quantification approaches, first, for individual defined benefit pension schemes on a stand-alone basis and then for the pension sector as a whole by quantifying economic capital of the UK’s Pension Protection Fund, which takes over eligible schemes with deficit, in the event of sponsor insolvency. We find that economic capital requirements for individual schemes are significantly high. However, we show that sharing risks through the Pension Protection Fund reduces the aggregate economic capital requirement of the entire sector.

The analysis of causal mortality provides rich insight into changes in mortality trends that are hidden in population-level data. Therefore, we develop and apply a multinomial logistic framework to model causal mortality. We use internationally classified cause-of-death categories and data obtained from the World Health Organization. Inherent dependence amongst the competing causes is accounted for in the framework, which also allows us to investigate the effects of improvements in, or the elimination of, cause-specific mortality. This has applications to scenario-based forecasting often used to assess the impact of changes in mortality. The multinomial model is shown to be more conservative than commonly used approaches based on the force of mortality. We use the model to demonstrate the impact of cause-elimination on aggregate mortality using residual life expectancy and apply the model to a French case study.

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