In this paper, we explore potential surplus modelling improvements by investigating how well the available models describe an insurance risk process. To this end, we obtain and analyse a real-life data set that is provided by an anonymous insurer. Based on our analysis, we discover that both the purchasing process and the corresponding claim process have seasonal fluctuations. Some special events, such as public holidays, also have impact on these processes. In the existing literature, the seasonality is often stressed in the claim process, while the cash inflow usually assumes simple forms. We further suggest a possible way of modelling the dependence between these two processes. A preliminary analysis of the impact of these patterns on the surplus process is also conducted. As a result, we propose a surplus process model which utilises a non-homogeneous Poisson process for premium counts and a Cox process for claim counts that reflect the specific features of the data.

Fertility, particularly at its current low level in many developed countries and high level in some less developed countries, is a key factor driving demographic, economic, and societal changes at local, national, and global levels. Population ageing due to low fertility and increasing longevity represents one of the most significant global megatrends and risks. Many countries are already experiencing population decline and rapid growth of their elderly populations, with implications for workforce size, economic development, health and pension schemes, and social security arrangements. Actuaries are well known for their work on mortality and morbidity, but they have rarely considered fertility and its proximate determinants, despite their demographic and economic effects. This paper explores key explanations and outcomes of past and projected future fertility trends, and the implications for actuaries and for political and economic decision-makers.

This paper sets out the working party’s view that for a defined benefit pension scheme’s commutation rate the appropriate starting point should be to set it in line with the scheme’s cash equivalent transfer value basis. We recognise that there may be several reasons why an actuary in their advice may deviate from that starting point and we explore these in detail, giving our views on when deviation is and is not justified, noting that many common reasons used such as selection risk are often used without (in our view) adequate justification. We also cover frequency of review – our view is that commutation rates should be reviewed at least every 3 years and actuaries should consider performing a high-level review of commutation rates annually. We suggest that actuaries should consider proposing market-related commutation rates especially in periods of volatile market conditions. In terms of timing, there are good arguments to review commutation terms either following or during a valuation. Finally, we set out some considerations on how actuaries should present their advice, such as clearly setting out all the information required to take key decisions, following up with any actuarial certification in writing (if necessary) and illustrating the impact on members for changing commutation rates.

Under the European Union’s Solvency II regulations, insurance firms are required to use a one-year VaR (Value at Risk) approach. This involves a one-year projection of the balance sheet and requires sufficient capital to be solvent in 99.5% of outcomes. The Solvency II Internal Model risk calibrations require annual changes in market indices/term structure/transitions for the estimation of the risk distribution for each of the Internal Model risk drivers.

Transition and default risk are typically modelled using transition matrices. To model this risk requires a model of transition matrices and how these can change from year to year. In this paper, four such models have been investigated and compared to the raw data they are calibrated to. The models investigated are:

• A bootstrapping approach – sampling from an historical data set with replacement.

• The Vašíček model was calibrated using the Belkin approach.

• The K-means model – a new non-parametric model produced using the K-means clustering algorithm.

• A two-factor model – a new parametric model, using two factors (instead of a single factor with the Vašíček) to represent each matrix.

The models are compared in several ways:

1. 1. A principal components analysis (PCA) approach that compares how closely the models move compared to the raw data.

2. 2. A backtesting approach that compares how each model’s extreme percentile compares to regulatory backtesting requirements.

3. 3. A commentary on the amount of expert judgement in each model.

4. 4. Model simplicity and breadth of uses are also commented on.

The Global Financial Crisis of 2007–2008 has elicited various debates, ranging from ethics over the stability of the banking system to subtle technical issues regarding the Gaussian and other copulas. We want to look at the crisis from a particular perspective. Credit derivatives have much in common with treaty reinsurance, including risk transfer via pooling and layering, scarce data, skewed distributions, and a limited number of specialised players in the market. This leads to a special mixture of mathematical/statistical and behavioural challenges. Reinsurers have been struggling to cope with these, not always successfully, but they have learned some lessons over the course of more than one century in business. This has led to certain rules being adopted by the reinsurance market and to a certain mindset being adopted by the individuals working in the industry. Some cultures established in the reinsurance world could possibly inspire markets like the credit derivatives market, but the subtle differences between the two worlds matter. We will see that traditional reinsurance has built-in incentives for (some) fairness, while securitisation can foster opportunism.

Mortality at older ages varies by season, increasing the uncertainty associated with modelling and projecting mortality at older ages and ultimately contributing to pension providers’ overall risk. As the population ages, it becomes more important to understand variations in seasonal mortality between pensioners and to identify those most vulnerable to seasonal mortality differences. Using data from the Self-Administered Pension Schemes mortality investigation of the Continuous Mortality Investigation of the Institute and Faculty of Actuaries, UK, this paper investigates variations in seasonal mortality amongst members of UK occupational pension schemes over the period 2000–2016. Results are also compared with the corresponding population of England and Wales. For the oldest age groups (80+), which are most affected by seasonality, females are more vulnerable to seasonal differences in mortality for each pensioner group relative to males. Following a long-term decline in the winter-summer mortality gap the gap increased over the period, particularly for female pensioners and dependants. Seasonality remains a feature of UK mortality at older ages and risk management for pension schemes should consider seasonality when analysing overall mortality experience.

Climate change is at the forefront of discussions for many companies. Climate change-related disclosures and reporting are important tools and allow stakeholders to understand climate-related risks a company is facing and help various stakeholders to take informed decisions.

The landscape for climate change-related reporting requirements is ever evolving, with a trend from voluntary to mandatory, with many global disclosure standards and requirements influencing local requirements and other related standards.

This paper explores these ideas further, giving a general background to disclosure requirements, discusses greenwashing, details disclosure organisations including TCFD and the ISSB, and provides details on a country level including green taxonomies.