Grant: Discovery Grants Program - Individual

One of the branches in actuarial science, called risk theory, analyzes important quantities related to the development of the surplus process of insurance companies. Such quantities are the probability of ruin, the deficit at the time of ruin, and the surplus immediately before ruin, for instance. These provide measures of the riskiness of the overall strategy of an insurance company. As a consequence, they suggest ways of improvement of the company's chances of avoiding insolvency (or ruin), as well as retaining competitive premium rates. Most models of insurance companies' surplus postulate that premiums are received at a constant rate in time. We propose to investigate alternative approaches such as varying premiums depending on the current surplus or depending on fluctuations of financial markets.