Actuarial Science and Insurance Education and events

Title:  Exploring the Impact of Precipitation on Short-Term Insurance Pricing in a Changing Climate.

Abstract:

Short-term insurance ((or property and casualty)  pricing traditionally relies on statistical methods like Generalised Linear Models and policyholder-specific rating factors to estimate expected claims costs associated with specific risk profiles. However, recent years have witnessed a growing influence of weather-related events in the industry, with the potential for amplification due to both climate change and meteorological phenomena like the El Niño–Southern Oscillation (ENSO) and La Niña.

In this talk, we directly link a dataset of buildings' risk exposure and associated claims to a high-resolution gridded precipitation dataset. The objective is to assess the predictive power of precipitation on both actual and forecasted bases. Our proposed modelling framework enables the estimation of both the frequency and severity of buildings' claims, considering the combined dataset. We evaluate the added precipitation feature's significance compared to traditionally used rating factors, exploring the sensitivity of claims frequency and severity to precipitation variations.

Through diverse precipitation scenarios, we demonstrate how quantifying the risks associated with excessive precipitation enables more accurate financial forecasts and facilitates the exploration of effective risk mitigation strategies.

Biography:

Rendani Mbuvha is the Google DeepMind Academic Fellow in Machine Learning at Queen Mary University of London and Associate Professor in Actuarial Science at the University of Witwatersrand, Johannesburg. He received his PhD from the University of Johannesburg in 2021 and a Masters in Machine Learning from KTH Royal Institute of Technology in Sweden. He is a fellow of the Institute and Faculty of Actuaries (UK) and holds the Chartered Enterprise Risk Actuary designation. Rendani’s current research interests lie in the intersection of probabilistic Machine Learning and climate risk modelling. He is a non-executive director of Bidvest Life and a trustee of Discovery Health Medical Scheme in South Africa. He is the author of the book "Hamiltonian Monte Carlo Methods in Machine Learning", and he is a previous recipient of the Google PhD fellowship.

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Title: Error analysis in simulation-based capital models:  removing approximation errors from capital estimates

Abstract:

Determining accurate capital requirements is an important activity in the life insurance industry. Within simulation based capital-models approximations are often introduced to speed-up Monte Carlo calculations that are used to form capital estimates. However, the resulting capital estimates contains both statistical and approximation errors. Understanding, and if possible eliminating these errors, is therefore of clear benefit to the insurance industry. This talk is based on two recent papers that show how error analysis can be applied to measure the propagation of approximation errors in representative capital models, and also how error analysis can be used to create calculation methods to completely eliminate approximation errors from capital estimates. Advances in the handling of approximation errors improve the accuracy of capital requirements.

Biography:

Dr Dan Crispin is Head of Risk Strategists at Rothesay, a UK life insurance company. In his current role he oversees the firm's modelling from a risk-orientated perspective. His recent research has focused on the application of formal error analysis to address current challenges in capital models. Dan has maintained an interest in optimization and analysis from his PhD studies in the calculus of variations.

You can download a copy of the seminar presentation here.

Title: Analysis of VIX-linked fee incentives in variable annuities via continuous-time Markov chain approximation

Abstract:

VIX-linked fees for variable annuities (VA) have been popular recently to better align the underlying volatility with incentives to deter early surrender of the VA contracts. We consider VA contracts in which the insurance fee is linked to the VIX index and study the impact of the fee structure on the optimal surrender strategy. Approximating the VA account value and the volatility processes by a two-layer continuous-time Markov chain allows us to work with various VIX-linked fee structures and a wide class of stochastic volatility models. We discuss a simple condition under which early surrenders are suboptimal, and present a fast algorithm to approximate the value of the VA contract when this condition is not satisfied. Extensive numerical examples are carried out to illustrate the impact of the fee structure on optimal policyholder behavior.

You can download a copy of the seminar presentation here.

Title: The role of the variance function in mean estimation and validation

Abstract:

Regression modeling for insurance pricing mostly focuses on mean estimation. Using a strictly consistent loss function implies that the mean estimates are asymptotically correct. However, this is a limiting statement and insurance prices are calculated on finite samples. It is known that under heteroskedasticity suitable variance estimates can significantly improve the regression model estimation. We investigate isotonic regression which is a nonparametric rank-preserving regression approach. This isotonic regression is used to (1) explore the power variance parameter of the variance function within Tweedie’s family of distributions, (2) derive a semi-parametric bootstrap under heteroskedasticity, (3) provide a test for autocalibration, (4) explore a quasi-likelihood approach to benefit from best-asymptotic estimation, (5) deal with several difficulties under lognormal assumptions. In all these problems we verify that variance estimation using an isotonic regression is very beneficial. The presentation is based on a paper with Mario Wüthrich.

Biograply:

Łukasz Delong is working as a full professor at the Faculty of Economic Sciences at University of Warsaw. He has PhD in Mathematics, Habilitation Degree in Economics and Professor title in Economics and Finance. He is an actuary with license no. 130 issued by the Polish Financial Supervision Authority, the Head of the Examination Committee for Actuaries at the Polish Financial Supervision Authority and a Board Member of the Polish Society of Actuaries. His scientific research includes different areas of actuarial mathematics with emphasis on stochastic modelling of financial risks and actuarial statistical learning. He is an editor of ASTIN Bulletin – The Journal of International Actuarial Association.

Title:  Survivor Dividend in Nonfinancial Defined Contribution (NDC) plans: Theoretical Basis and its Use as a Tool to Face Longevity Risk and Improve Pension Adequacy

Abstract:

The mechanisms of nonfinancial defined contribution pension schemes (NDCs) are close to those of a fully funded defined contribution plan but under a pay-as-you-go framework. Of particular interest is how the accumulated capita of a deceased person is used, when the death occurs prior to retirement. At the moment, Sweden is the only NDC country that distributes this capital,called survivor dividend (SD) among the same cohort survivors. Without a distribution of the SD the scheme would accumulate a reserve with no clear purpose.

This research develops a model to show whether it would be justified to include the survivor dividend in the calculation of affiliate pension balances. Secondly, in the case of non-inclusion, we analyse to what extent the SD kept by NDCs can be used to cover an unexpected longevity increase. Lastly, we study whether the SD can be used to improve pension adequacy giving low-income pensioners the financial support they need.

Our findings show that the survivor dividend has a strong financial basis in the pension calculation which enables the macro contribution rate applied to be the same as the individual credited rate.  In the case of non-distribution among the cohort survivors, our results indicate that the survivor dividend can be used to set up a minimum pension that benefit 66% of the pensioners increasing the average annual pension by 9.65%.

Biography:

Prof Carmen Boado-Penas (Heriot-Watt) applies actuarial mathematics to study the sustainability of pension systems. In 2009, she was awarded a prize by the Foundation of Spanish Savings Banks for her PhD ’Instruments for improving the equity, transparency and sustainability of pay-as-you-go pension systems’. She has published more than 40 peer-reviewed papers on public pension systems in prestigious international journals and has cooperated on various projects at the Swedish Social Insurance Agency in Stockholm and at the Spanish Ministry of Labour and Immigration. In 2012, she worked as head of research on a project for the Spanish Ministry of Labour and Immigration, the aim of which was to evaluate the redistributive effects of the pension system reform in Spain. In 2020, she received the BBVA Longevia award to support pension research.

Title:  Fairness through regularization: an approach to mitigate group disparities for multiple protected features.

Biography

Benjamin Avanzi PhD Actuary SAA CERA GAICD is Professor of Actuarial Studies at the University of Melbourne. He worked as an actuarial consultant in Switzerland and Canada, was Executive Chairman of the Board of a Swiss pension fund from 2006 to 2008, and held full-time academic positions in Australia and Canada since 2008.  He is currently on the Management Board of the Theatre Royal (Hobart, Tasmania).

Benjamin is an "Actuary SAA" with the Swiss Association of Actuaries (fully qualified actuary, equivalent to Fellow in Switzerland), an Affiliate member of the Australian Actuaries Institute, an Academic member of the Casualty Actuarial Society, as well as a member of the ASTIN section of the IAA. He is also a Chartered Enterprise Risk Actuary (CERA) and a Graduate member of the Australian Institute of Company Directors (GAICD).

Benjamin has published numerous papers in top actuarial and operations management journals. He was awarded (along with co-authors) the Hachemeister Prize twice by the Casualty Actuarial Society in 2017 and 2023, the Taylor Fry General Insurance Seminar Silver Prize in 2018, and a Highly Commended Paper Prize by the Institute and Faculty of Actuaries in 2022. He is an Editor of the ASTIN Bulletin, an Associate Editor of Insurance: Mathematics and Economics, as well as a member of the Editorial Board of the open access journal Risks.

Abstract

Ensuring fairness in machine learning models is essential for their application in various fields, particularly in decision-making processes that impact individuals. Recent advancements in machine learning have led to the development of complex models that achieve high predictive accuracy but have also revealed latent societal inequalities in decision-making processes that may have detrimental effects on certain sub-groups in society.

The concept of fairness in machine learning is complex and varies depending on the legal framework and cultural norms. Typically, fairness is mathematically encoded into a set of criteria. Group-level fairness criteria, such as demographic parity, equal opportunity, and equalized odds, emphasize the promotion of equitable treatment among various groups, particularly those identified by protected characteristics like race, gender, or age.  On the other hand, individual-level fairness ensures that individuals with similar characteristics receive similar treatment.

A significant portion of the literature on fairness centers around simple binary classification problems, where the protected feature is usually coded as binary [3]. For instance, the widely used COMPAS software in the US, designed to determine the likelihood of reoffending by inmates, has been thoroughly investigated after being found to be biased against African American individuals. While the focus is primarily on binary classification, there are also cases where regression tasks are affected by a lack of fairness, including insurance pricing [5]. In fact, the European Union Directive 2004/113/EC in conjunction with the Guidelines on the application of Council Directive 2012/C 11/01 prohibits insurance instruments from being priced differently based solely on gender differences.

Scenarios can become more complex; e.g., insurance pricing needs to be performed without considering gender differences while avoiding the use of cultural and racial origin. In such cases, it has been observed that even models constructed to be race- and gender-neutral can still discriminate within subcategories. For example, Black males may receive different treatment than White females, known as intersectional unfairness.

This paper considers data that display latent inequalities and proposes a novel regularization approach based ondistance covariance, that aims to reduce their effect on model output while adhering to a pre-specified fairness criterion, such as demographic parity. The regularizer is compatible with both regression and classification tasks and can be applied to any modeling approach that optimizes an objective. Furthermore, unlike existing methodologies, it allows for the mitigation of multiple protected features of any type, such as categorical or continuous, mitigating the impact
of differences within protected (intersectional) subgroups.

The methodology presented in this study performs competitively with some of the state-of-the-art methods that address a single protected feature. It also offers a ready-to-use statistical test that can be used to calibrate the regularization parameter and validate the satisfaction of the fairness criterion. Moreover, it can be extended to account for multiple protected features jointly, performing well in equal treatment of protected (intersectional) subgroup.