This paper introduces a new pension contract which provides a smoothed return for the customer. The new contract protects customers from adverse asset price movements while keeping the potential of positive returns. It has a transparent structure and clear distribution rule, which can be easily understood by the customer. We compare the new contract to two other contracts under Cumulative Prospect Theory (CPT); one has a similar product structure but without guarantees and the other provides the same guarantee rate but with a different structure. The results show that the new contract is the most attractive contract for a CPT-maximising customer. Yet, we find different results if we let the customer be an Expected Utility Theory-maximising one. Moreover, this paper presents the static optimal portfolio for an individual customer. The results conform to the traditional pension advice that young people should invest more of their money in risky assets while older people should put more money in less risky assets.

This paper adopts an actuarial approach to identify the risk factors of government-funded maternal out-of-hospital costs in Australia, with a focus on women who experience adverse birth outcomes. We use a two-phase modelling methodology incorporating both classification and regression trees and generalised linear models on a data set that links administrative and longitudinal survey data from a large sample of women, to address maternal out-of-hospital costs. We find that adverse births are a statistically significant risk factor of out-of-hospital costs in both the delivery and postnatal periods. Furthermore, other significant cost risk factors are in-vitro fertilisation, specialist use, general practitioner use, area of residence and mental health factors (including anxiety, intense anxiety, postnatal depression and stress about own health) and the results vary by perinatal sub-period and the patient’s private health insurance status. We highlight these differences and use the results as an evidence base to inform public policy. Mental health policy is identified as a priority area for further investigation due to the dominance of these factors in many of the fitted models.

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.

This paper starts with the Beta transform and discusses the stochastic ordering properties of this transform under different parameter settings. Later, the distribution of discounted aggregate claims in a compound renewal risk model with dependence between inter-claim times and claim sizes is studied. Recursive formulas for moments and joint moments are expressed in terms of the Beta transform of the inter-claim times and claim severities. Particularly, our moments formula is more explicit and computation-friendly than earlier ones in the references. Lastly, numerical examples are provided to illustrate our results.

Insurance regulation often dictates that insurers monitor their solvency risk in real time and take appropriate actions whenever the risk exceeds their tolerance level. Bayesian methods are appealing for prediction problems thanks to their ability to naturally incorporate both sample variability and parameter uncertainty into a predictive distribution. However, handling data arriving in real time requires a flexible non-parametric model, and the Monte Carlo methods necessary to evaluate the predictive distribution in such cases are not recursive and can be too expensive to rerun each time new data arrives. In this paper, we apply a recently developed alternative perspective on Bayesian prediction based on copulas. This approach facilitates recursive Bayesian prediction without computing a posterior, allowing insurers to perform real-time updating of risk measures to assess solvency risk, and providing them with a tool for carrying out dynamic risk management strategies in today’s “big data” era.

In this paper, we study the optimal proportional reinsurance problem in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component, and the criterion is to minimise the probability of drawdown, namely, the probability that the value of the surplus process reaches some fixed proportion of its maximum value to date. By the method of maximising the ratio of drift of a diffusion divided to its volatility squared, and the technique of stochastic control theory and the corresponding Hamilton–Jacobi–Bellman equation, we investigate the optimisation problem in two different cases. Furthermore, we constrain the reinsurance proportion in the interval [0,1] for each case, and derive the explicit expressions of the optimal proportional reinsurance strategy and the minimum probability of drawdown. Finally, some numerical examples are presented to show the impact of model parameters on the optimal results.

Operational risk events in banks include extreme events with significant losses being incurred and with substantial impact on share prices. A pooling arrangement between banks that would be able to reduce overall costs and reduce share price impacts would seem desirable, but one of the major inhibiting factors to establish the feasibility of such a pooling arrangement is that statistical models of these extreme events are difficult to build with any reliability. This paper uses both quantitative and qualitative analysis of operational risk losses for EU and US banks over the period 2008–2014 to establish the feasibility of creating a pooling arrangement between the banks and concludes that such an arrangement might be feasible but would require compulsory membership of the pool and capping of losses.

Heavy-tailed distributions have been observed for various financial risks and papers have observed that these heavy-tailed distributions are power law distributions. The breakdown of a power law distribution is also seen as an indicator of a tipping point being reached and a system then moves from stability through instability to a new equilibrium. In this paper, we analyse the distribution of operational risk losses in US banks, credit defaults in US corporates and market risk events in the US during the global financial crisis (GFC). We conclude that market risk and credit risk do not follow a power law distribution, and even though operational risk follows a power law distribution, there is a better distribution fit for operational risk. We also conclude that whilst there is evidence that credit defaults and market risks did reach a tipping point, operational risk losses did not. We conclude that the government intervention in the banking system during the GFC was a possible cause of banks avoiding a tipping point.

In this paper we develop a vector autoregressive model for retail prices and wages within the Wilkie model. The results turn out to be a slight improvement over the original model, but the simulated results are not very different.

In this study, we show how expressions for the probability of ultimate ruin can be obtained from the probability function of the time of ruin in a particular compound binomial risk model, and from the density of the time of ruin in a particular Sparre Andersen risk model. In each case evaluation of generalised binomial series is required, and the argument of each series has a common form. We evaluate these series by creating an identity based on the generalised negative binomial distribution. We also show how the same ideas apply to the probability function of the number of claims in a particular Sparre Andersen model.

The global banking system can be shown to be a Complex Adaptive System that exhibits phase transitions from time to time. These phase transitions can result in significant financial losses to the community that we estimate to be much more significant than losses occurring during “business as usual” periods. In this paper, we argue that the significant losses arising from phase transitions in the banking system requires a very different approach to regulation than the current Basel regime, and that there is a need to transition the Basel regime from a Federation of Systems to a System of Systems. We demonstrate that the World Health Organisation’s recent management system for pandemics is ideally suited for management of the global banking system and would have greater potential to control the phase transition losses than the current Basel system.

Cohort effects are important factors in determining the evolution of human mortality for certain countries. Extensions of dynamic mortality models with cohort features have been proposed in the literature to account for these factors under the generalised linear modelling framework. In this paper we approach the problem of mortality modelling with cohort factors incorporated through a novel formulation under a state-space methodology. In the process we demonstrate that cohort factors can be formulated naturally under the state-space framework, despite the fact that cohort factors are indexed according to year-of-birth rather than year. Bayesian inference for cohort models in a state-space formulation is then developed based on an efficient Markov chain Monte Carlo sampler, allowing for the quantification of parameter uncertainty in cohort models and resulting mortality forecasts that are used for life expectancy and life table constructions. The effectiveness of our approach is examined through comprehensive empirical studies involving male and female populations from various countries. Our results show that cohort patterns are present for certain countries that we studied and the inclusion of cohort factors are crucial in capturing these phenomena, thus highlighting the benefits of introducing cohort models in the state-space framework. Forecasting of cohort models is also discussed in light of the projection of cohort factors.

Rapid population ageing in China has urged the need to understand health transitions of older Chinese to assist the development of social security programmes and financial products aimed at funding long-term care. In this paper, we develop a new flexible approach to modelling health transitions in a multi-state Markov model that allows for age effects, time trends and age-time interactions. The model is implemented in the generalised linear modelling framework. We apply the model to evaluate health transitions of Chinese elderly using individual-level panel data from the Chinese Longitudinal Healthy Longevity Survey for the period 1998–2012. Our results confirm that time trends and age–time interactions are important factors explaining health transitions in addition to the more commonly used age effects. We document that differences in disability and mortality rates continue to persist between urban and rural older Chinese. We also compute life expectancies and healthy life expectancies based on the proposed model as inputs for the development of aged care and financial services for older Chinese.

The chain-ladder method is one of the most popular claims reserving techniques. The aim of this study is to back-test the chain-ladder method. For this purpose, we use a stochastic scenario generator that allows us to simulate arbitrarily many upper claims reserving triangles of similar characteristics for which we also know the corresponding lower triangles. Based on these simulated triangles, we analyse the performance of the chain-ladder claims reserving method.

The financial system can be shown to be a complex adaptive system consisting primarily of a federation of systems and systems of systems. There are significant similarities between the characteristics of natural systems and financial systems suggesting that the type of analysis employed in understanding natural systems could have application in financial system analysis. Cladistics analysis has been used extensively for analysis of biological systems and has accordingly been used in the social sciences for some years but a rigorous justification for adopting the analysis has not been undertaken. This paper discusses the appropriateness of applying cladistics analysis to financial systems, and then considers the appropriate methodology to be adopted for analysis of different financial events.

In this paper, we carry out an investigation on modelling basis risk and measuring risk reduction in a longevity hedge constructed by index-based longevity swaps. We derive the fitting procedures of the M7-M5 and common age effect+Cohorts models and define the level of longevity risk reduction. Based on a wide range of hedging scenarios of pension plans, we find that the risk reduction levels are often around 50%–80% for a large plan, while the risk reduction estimates are usually smaller than 50% for a small plan. Moreover, index-based hedging looks more effective under a more precise hedging scheme. We also perform a detailed sensitivity analysis on the hedging results. The most important modelling features are the behaviour of simulated future variability, portfolio size, speed of reaching coherence, data size and characteristics, simulation method, and mortality structural changes.

Pay-how-you-drive (PHYD) or usage-based (UB) systems for automobile insurance provide actuaries with behavioural risk factors, such as the time of the day, average speeds and other driving habits. These data are collected while the contract is in force with the help of telematic devices installed in the vehicle. They thus fall in the category of a posteriori information that becomes available after contract initiation. For this reason, they must be included in the actuarial pricing by means of credibility updating mechanisms instead of being incorporated in the score as ordinary a priori observable features. This paper proposes the use of multivariate mixed models to describe the joint dynamics of telematics data and claim frequencies. Future premiums, incorporating past experience can then be determined using the predictive distribution of claim characteristics given past history. This approach allows the actuary to deal with the variety of situations encountered in insurance practice, ranging from new drivers without telematics record to contracts with different seniority and drivers using their vehicle to different extent, generating varied volumes of telematics data.

In this paper, we model the surplus process as a compound Poisson process perturbed by diffusion and allow the insurer to ask its customers for input to minimize the distance from some prescribed target path and the total discounted cost on a fixed interval. The problem is reduced to a version of a linear quadratic regulator under jump-diffusion processes. It is treated using three methods: dynamic programming, completion of square and the stochastic maximum principle. The analytic solutions to the optimal control and the corresponding optimal value function are obtained.

This paper presents methods for generating new distortion functions utilising distribution functions and composite distribution functions. To ensure the coherency of the corresponding distortion risk measures, the concavity of the proposed distortion functions is established by restricting the parameter space of the generating distribution. Closed-form expressions for risk measures are derived for some cases. Numerical and graphical results are presented to demonstrate the effects of parameter values on the risk measures for exponential, Pareto and log-normal losses. In addition, we apply the proposed distortion functions to derive risk measures for a segregated fund guarantee.