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 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.

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.

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.

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.

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.

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.