A black swan in the insurance sector can be a widespread and unusually destructive event that results in exceptionally large compensation sums. Such occurrences include natural disasters like extensive forest fires or powerful storms whose prevalence has increased due to climate change.
Miriam Hägele’s doctoral thesis entitled ‘On multivariate heavy-tailed risk modelling in insurance and finance’ was examined at the University of Helsinki on 22 October 2022. The thesis analyses the nature of multivariate risks with the help of mathematical models, providing solutions to current problems in the insurance sector.
Will companies stay afloat?
Companies in the insurance and financial sector face a range of risks. Some of them can be easily estimated and modelled, but there are also others that are unpredictable.
Past financial crises show that commonly used models and tools are not always sufficient to model large risks. For example, unexpectedly substantial losses can easily result in large claims leading to the insolvency of the insurance company.
Catastrophic events, such as earthquakes, floods, pandemics, terrorist attacks and cyberattacks wreak large-scale havoc that generate exceptionally large costs for insurance and reinsurance companies.
“Observations and existing data are not always enough to predict extreme phenomena in the future, since the world is changing and the available useful data on predictable phenomena is insufficient,” says Miriam Hägele.
For example, climate change is bringing about new kinds of natural disasters, including increasingly extensive forest fires and intense storms. In the financial markets, the return rates of stock portfolios have similar characteristics. Often, the fluctuations are low and the return rates are in line with forecasts, but stock market crashes are possible. This is why there is a demand for models that take into consideration both minor average fluctuation as well as major extreme events.
“Mathematically, these requirements are met by what are known as heavy-tailed distributions. They are distributions whose tails are not exponentially bounded, making extreme events possible in practice,” Hägele says.
As a rule, insurance companies offer a range of policies and operate in a variety of sections. Consequently, the companies must not only assess the risks of different lines of business separately, but also take into consideration their interactions and dependencies when assessing the company’s solvency. For example, instead of affecting one type of insurance, earthquakes can result in large claims associated with several insurance types.
In the doctoral thesis, the yearly net payout of an insurance company is examined as a stochastic process based on heavy-tailed random vectors, enabling the modelling of the company’s solvency in the long term.
The thesis also introduces a method for identifying the lines of business with the highest risk and a strategy for balancing related risks with the help of reinsurance.
From student to mathematician
Miriam Hägele, who is originally from Germany, began studying mathematics in her home country in 2011, familiarising herself with the University of Helsinki during a year of student exchange. She returned to Helsinki to complete her master’s studies, specialising in insurance mathematics, as it allows the practical application of mathematics in a way that benefits society. Unique in Finland, the University of Helsinki offers a specialisation option in insurance and financial mathematics, with the opportunity to complete the entire master’s degree and postgraduate studies in the field of insurance mathematics.
“Employment is also certain in the field,” Hägele chuckles, recommending it to other students of mathematics. Already during her studies, Hägele had a summer job at the Finnish Centre for Pensions, where she found a job as a full-time mathematician after graduation.
She is also pursuing an actuary certification by the Ministry of Social Affairs and Health. According to the Insurance Companies Act, Finnish insurance companies must have an actuary responsible for drawing up actuarial calculations and reports. These positions require skills in mathematics provided by courses in the University of Helsinki’s specialisation option in insurance and financial mathematics. In addition, for example legislative knowledge and work experience in the insurance sector are needed.
Miriam Hägele, phone. +358 504732860, firstname.lastname@example.org