Fast and accurate simulation of randomness

Many processes in the real world are driven by random phenomena. And when trying to anticipate risks, whether in the field of finance, neurobiology, or engineering for instance, it is of utmost importance to be able to account for as many scenarios as possible. To model random phenomena, mathematical analysts use equations that not only describe the changes over time – through the use of differential equations –, but also incorporate an element of randomness. Recognising that current methods used to solve these so called stochastic differential equations in the insurance and financial industry might present tremendous errors, Dr. Michaela Szölgyenyi aims to provide a new and more evolved approach. The global objective of her research is to enable more accurate simulations that help understand various risks in the insurance and financial market.

A timely example of how crucial accurate modelling of random phenomena can be, is the impact of interest rates on the life-insurance sector, which provides for payment of a stipulated sum of money at the end of a set period of time or upon death of the insured. « Being able to better account for interest rate risk is particularly important under tough market conditions like the ones we face nowadays », says Dr. Michaela Szölgyenyi. Life insurers "borrow" from policy owners and invest to generate returns through investment income and capital gains. Therefore, interest rates are a key performance driver for life insurance companies. « The problem is that existing models for interest rates are too complicated for real world applications », the researcher points out. « There is a gap between what is feasible theoretically and in practice. The real world is not as clean as the one in literature ».

Transforming current methods to adjust it to real world applications »

Dr. Michaela Szölgyenyi’s project seeks to address two sets of issues regarding modelling of randomness : reliability and computation time. « When we want to know how processes are likely to behave in the future, not only do we need a method which is able to do the simulation, but we also need to know that we can trust the results and know what the error margin is », Dr. Michaela Szölgyenyi. « Another aspect is that we need to obtain these reliable results after a reasonable amount of time ». « For instance, current methods used to model the evolution of stock prices work on paper, but they require enormous amounts of computation time ». « People still use them but they get wrong results », she regrets. To address these shortfalls and develop more evolved models, Dr. Michaela Szölgyenyi and her mentor, Professor Arnulf Jentzen, are using a careful blend of existing ideas – ones that have not been applied to this issue in the past –, as well as a novel toolkit.

Dr. Michaela Szölgyenyi’s work will close a part of the gap in the academic literature in the field, and it will have a direct impact on many applications. The computability of solutions to these stochastic differential equations is indeed essential for performing simulation studies that help to understand the risks in the market and also to price these risks correctly.