Quantum Computing for the Calculation of Solvency Capital Requirements

Since the EU introduced the Solvency II Directive in 2016, insurers in Europe have had to calculate their solvency capital requirements. This is the amount of reserves that the insurer must hold in order to guarantee its solvency for the next year with a high degree of probability. According to the regulations, the solvency capital requirement must be determined on the basis of the entire loss distribution. The Monte Carlo simulations required for this are particularly time-consuming - even if they can be highly parallelized - so that they are (or can only be) carried out once a year as a rule.

We are investigating how various quantum computing algorithms can support and accelerate these calculations. A particular focus here is on amplitude estimation and quantum machine learning.

Amplitude estimation has a similar field of application to Monte Carlo methods, but promises a quadratically faster convergence rate. This method can be used to calculate options, an important part of determining solvency capital.

Regression Model for Approximation  

Regression models for approximating the solvency capital requirement are an active area of research. A major problem here is that the generation of training data is very time-consuming and therefore expensive. There is hope that quantum machine learning approaches will be able to generalize better than classic machine learning methods from a small amount of data.