This paper outlines a framework for explicitly including ethics in actuarial education. The framework includes integrity, the cardinal virtues (justice, prudence, self-control and courage), and vocation. It is based on a traditional understanding of ethics, and it is argued that it has the potential to be widely acceptable. Justification, from philosophy, is found mainly in virtue ethics, and the work of Alasdair MacIntyre. The framework is concerned with matters of character as well as behaviour and ultimate outcomes (which are the respective concerns of apparently competing deontological and teleological theories). Integrity and the cardinal virtues can be found within current professional standards or, it is argued in the case of courage, should be there. We come to appreciate and display the virtues as we are inducted into a professional community by teachers and mentors. Our view of ethics is incomplete, however, without acknowledgement of our own weaknesses and failures, and an understanding of the role of regulation. Such understanding should include insight into the way in which ideologies and institutions can pervert ethics for the benefit of vested interests. Finally, suggestions are made as to how the framework of the virtues can be included in the actuarial syllabuses.

The conditions under which pension schemes merge is an important issue which has been under-researched. Mergers can affect the strength of the sponsor's covenant and the balance of power between the trustees and the sponsor, as well as the deficit or the surplus of the receiving scheme and its funding ratio. This paper sets out two financial criteria to be met by any pension scheme merger: no profit or loss on merging with another scheme; and no dilution of the funding ratio. After defining a merger basis for valuing the assets and liabilities, and allowing for adjustments to the funding ratio via side receipts and payments; it is shown that, whether or not these criteria are met, depends on the state of the financial markets.

This paper presents the findings of a survey of the current Dynamic Financial Analysis (DFA)/Financial Condition Report (FCR) practices in the United Kingdom general insurance industry. An independent samples t test for non-respondent bias was conducted, and the results suggest that the respondent sample is representative of the survey population. The survey results revealed: (1) that the use of DFA techniques in the industry was limited; (2) that scenario testing was the most frequently used technique; (3) that the most common DFA application was the evaluation of reinsurance programmes; (4) that less than ten scenarios were run regularly; (5) that inflation was the most frequently modelled economic variable; (6) that the capability of asset modelling of general insurers was restricted; (7) that the most common method of liability modelling was to use all in force policies in aggregate; (8) that the most common projection periods in DFA and business planning were three years; (9) that the main reason for not using DFA techniques and producing FCR was lack of need; and (10) that views on whether a Guidance Note on FCR specifically for general insurers should be introduced differed.

In this paper, we present an extension of the model proposed by Lin & Liu that uses the concept of physiological age to model the ageing process by using phase-type distributions to calculate the probability of death. We propose a finite-state Markov jump process to model the hypothetical ageing process in which it is possible the transition rates between non-consecutive physiological ages. Since the Markov process has only a single absorbing state, the death time follows a phase-type distribution. Thus, to build a mortality table the challenge is to estimate this matrix based on the records of the ageing process. Considering the nature of the data, we consider two cases: having continuous time information of the ageing process, and the more interesting and realistic case, having reports of the process just in determined times. If the ageing process is only observed at discrete time points we have a missing data problem, thus, we use a stochastic Expectation–Maximisation (SEM) algorithm to find the maximum likelihood estimator of the intensity matrix. And in order to do that, we build Markov bridges which are sampled using the Bisection method. The theory is illustrated by a simulation study and used to fit real data.

The implications of genetic testing information availability for society, medicine, employment, and individual privacy rights have generated much political debate, legislation and academic research. Part of this debate centres on the ethical and economic considerations resultant from this expanded knowledge, particularly for insurance practices. Within insurance economics, the possibility of adverse selection has been debated and the potential for a ban on an insurer's use of genetic testing has been studied with respect to whether or not such a ban might actually result in insurance market failure due to this adverse selection. Studies have examined the issue using expected loss cost (actuarial or ‘fair’) pricing models, and have not considered either equilibrium (supply and demand) price setting as is present in markets, or the potentially swamping effect of background health care risks facing the insured, having nothing to do with any particular genetic mutation. Here we construct a supply and demand function with both high and low risk individuals in the presence of background health care cost risks, and derive an equilibrium price and market composition to determine whether, if genetic information is allowed for individuals, but this same information is not shared with insurers: (1) is market failure inevitable? (it is not if the background risk is sufficiently high relative to potential genetic risk costs); (2) will equilibrium prices result in all low risk insured exiting the market? (not in the presence of significant background risk); and (3) how much would prices increase and market sales decrease if insurers do not have the same genetic information as the insured? (prices will increase, but not necessarily very much in the presence of background risk, and not as much as that previously estimated in the insurance literature).

The liquidity premium on corporate bonds has been high on the agenda of Solvency regulators owing to its potential relationship to an additional discount factor on long-dated insurance liabilities. We analyse components of the credit spread as a function of standard bond characteristics during 2003–2014 on a daily basis by regression analyses, after introducing a new liquidity proxy. We derive daily distributions of illiquidity contributions to the credit spread at the individual bond level and find that liquidity premia were close to zero just before the financial crisis. We observe the time-varying nature of liquidity premia as well as a widening in the daily distribution in the years after the credit crunch. We find evidence to support higher liquidity premia, on average, on bonds of lower credit quality. The evolution of model parameters is economically intuitive and brings additional insight into investors’ behaviour. The frequent and bond-level estimation of liquidity premia, combined with few data restrictions makes the approach suitable for ALM modelling, especially when future work is directed towards arriving at forward-looking estimates at both the aggregate and bond-specific level.

This paper proposes a two-phase deep reinforcement learning approach, for hedging variable annuity contracts with both GMMB and GMDB riders, which can address model miscalibration in Black-Scholes financial and constant force of mortality actuarial market environments. In the training phase, an infant reinforcement learning agent interacts with a pre-designed training environment, collects sequential anchor-hedging reward signals, and gradually learns how to hedge the contracts. As expected, after a sufficient number of training steps, the trained reinforcement learning agent hedges, in the training environment, equally well as the correct Delta while outperforms misspecified Deltas. In the online learning phase, the trained reinforcement learning agent interacts with the market environment in real time, collects single terminal reward signals, and self-revises its hedging strategy. The hedging performance of the further trained reinforcement learning agent is demonstrated via an illustrative example on a rolling basis to reveal the self-revision capability on the hedging strategy by online learning.

In this article, we explore the use of multivariate Archimedean copulas in modelling the mortality dependence between different countries and pricing mortality bonds. We study the fitting performance of multi-dimensional, fully nested, and partially nested Archimedean copulas and test 11 types of generators and two skewed distributions. To evaluate their practical usefulness, we adopt the fitted models to compute the market prices for some typical mortality bond structures. The results show that the copula assumption has a significant impact on the calculation of the prices of mortality-linked securities and the management of extreme mortality risks.

This paper proposes a shift in the valuation and production of long-term annuities, away from the classical risk-neutral methodology towards a methodology using the real-world probability measure. The proposed production method is applied to three examples of annuity products, one having annual payments linked to a mortality index and the savings account and the others having annual payments linked to a mortality index and an equity index with a guarantee that is linked to the same mortality index and the savings account. Out-of-sample hedge simulations demonstrate the effectiveness of the proposed less-expensive production method. In contrast to classical risk-neutral production, which revolves around the savings account as reference unit, the long-term best-performing portfolio, the numéraire portfolio of the equity market, is employed as the fundamental reference unit in the production of the annuity. The numéraire portfolio is the strictly positive, tradable portfolio that when used as denominator or benchmark makes all benchmarked non-negative portfolios supermartingales. Under real-world valuation, the initial benchmarked value of a benchmarked contingent claim equals its real-world conditional expectation. The proposed real-world valuation and production can lead to significantly lower values of long-term annuities and their less-expensive production than suggested by the risk-neutral approach.

The European-centric Solvency II and Australian-centric Life and General Insurance Capital regimes are two examples of risk-based approaches to capital determination and risk management for life insurers. Both consist of a three-pillar structure covering capital, risk management and disclosure requirements. We apply the capital requirements of each regime to three synthetic sets of insurance policies, including a risk, annuity and combined portfolios, and consider the impact on capital arising from three separate and relatively severe stress events. Results highlight the relatively capital intensive nature of annuities, the differences between different capital regimes, the significance of solvency II’s matching adjustment and the robustness of each regime to both pandemic and economic stresses. Results also highlight the nature of diversification benefits from within each capital regime, on overall capital requirements.

In this paper, we extend the optimality of the barrier strategy for the dividend payment problem to the setting that the underlying surplus process is a spectrally negative Lévy process and the discounting factor is an exponential Lévy process. The proof of the main result uses the fluctuation identities of spectrally negative Lévy processes. This extends recent results of Eisenberg for the case where the accumulated interest rate and surplus process are independent Brownian motions with drift.

Crop index microinsurance is a novel product that has been piloted and implemented in many developing countries. We attempt to give an overview of crop index microinsurance, covering the major issues needed to design, price and implement a crop index microinurance programme. In some ways, providing insurance to the poor is fundamentally different to providing insurance to the middle-income or rich; in other ways, including in the actuarial fields of product design, pricing and risk financing, there are strong similarities. We offer a stylised discussion of these differences and similarities, with particular reference to issues of potential interest to actuaries, and propose an actuarial framework for crop index microinsurance. Case studies from Malawi and the Philippines provide examples for what does and what does not seem to work in crop index microinsurance, and motivation for further work needed.

Traditionally, actuaries make their predictions based on simple, robust methods. Stochastic models become increasingly popular because they can enrich the point estimates with error estimates or even provide the whole probability distribution. Here, we construct such a model for German inpatient health expenses per age using the functional data approach. This allows us to see in which age groups the expenses change the most and where predictions are most uncertain. Jumps in the derived model parameters indicate that 3 years might be outliers. In fact, they can be explained by changes in the reimbursement system and must be dealt with. As an application, we compute the probability distribution of the total health expenses in the upcoming years.

We present an application of statistical graphical models to simulate economic variables for the purpose of risk calculations over long time horizons. We show that this approach is relatively easy to implement, and argue that it is appealing because of the transparent yet flexible means of achieving dimension reduction when many variables must be modelled. Using the United Kingdom data as an example, we demonstrate the development of an economic scenario generator that can be used by life insurance companies and pension funds.We compare different algorithms to select a graphical model, based on p-values, AIC, BIC and deviance. We find the economic scenario generator to yield reasonable results and relatively stable structures in our example, suggesting that it would be beneficial for actuaries to include graphical models in their toolkit.

Conditional mean risk sharing appears to be effective to distribute total losses amongst participants within an insurance pool. This paper develops analytical results for this allocation rule in the individual risk model with dependence induced by the respective position within a graph. Precisely, losses are modelled by zero-augmented random variables whose joint occurrence distribution and individual claim amount distributions are based on network structures and can be characterised by graphical models. The Ising model is adopted for occurrences and loss amounts obey decomposable graphical models that are specific to each participant. Two graphical structures are thus used: the first one to describe the contagion amongst member units within the insurance pool and the second one to model the spread of losses inside each participating unit. The proposed individual risk model is typically useful for modelling operational risks, catastrophic risks or cybersecurity risks.

In the classical collective model over a fixed time period of two insurance portfolios, we are interested, in this contribution, in the models that relate to the joint distribution F of the largest claim amounts observed in both insurance portfolios. Specifically, we consider the tractable model where the claim counting random variable N follows a discrete-stable distribution with parameters (α,λ). We investigate the dependence property of F with respect to both parameters α and λ. Furthermore, we present several applications of the new model to concrete insurance data sets and assess the fit of our new model with respect to other models already considered in some recent contributions. We can see that our model performs well with respect to most data sets.

In this paper, we conduct the study of long-term age-sex-specific mortality forecasting for subpopulations in different areas of China: cities, towns and counties. We use a modified CMI (Continuous Mortality Investigation) Mortality Projections Model, which has been discussed in Huang & Browne (Paper I), for modelling purposes. From the historical experience, we find that people in cities have lower mortality rates and higher mortality improvement rates than people in towns and counties for most ages. If this trend continues, the mortality of different areas will diverge further in the future. From the projection results, we find that there will be significant mortality and life expectancy differences between cities, towns and counties for both males and females. Sensitivity analysis for long-term rates of mortality improvement and the speed of convergence from “initial” to “long-term” rates of mortality improvement are conducted. Uncertainties are attached to the central estimates to overcome the limitation of the original CMI approach from which only deterministic results can be obtained.

Høgh, Linton and Nielsen (2006) showed that the famous result in the award winning paper of Froot and Stein (1998) is not correct in the sense that their result does not follow from their assumptions. In this paper we show that the economic intuition behind the paper of Froot and Stein (1998) is correct and that their result can be obtained when the market is reformulated in a continuous time setting and modern market theory is employed.

To gain insight into the use of Dynamic Solvency Testing (DST) and Financial Condition Reporting (FCR), a questionnaire was distributed to Appointed Actuaries in United Kingdom life offices. The response rate of the main survey was 76%. An independent-samples t-test for non-respondent bias was conducted and the results suggest that the respondent sample is representative of the survey population. Results from the 62 firms responding revealed: (1) Scenario testing was the most commonly used DST techniques. (2) Most life offices regularly run less than ten scenarios in scenario testing. (3) Most life offices reported using a five-year forecast period in DST. (4) The two most commonly seen difficulties are: difficulties in communicating complex issues to non-specialists, and how to present extremely adverse scenarios without causing undue concern. (5) Nearly all life offices use FCR. (6) Guidance Note 2 is generally considered acceptable. (7) Compared with the results reported by previous studies, the use of DST techniques is now more common in life offices. (8) There is a significant difference in DST/FCR practices between with-profits and non-profit offices.