Grant: Discovery Grants Program - Individual

Risk management requires that an insurance company consider the possibility of experiencing adverse claims while satisfying its shareholders with, for instance, dividend payments. For a financial institution, accurate pricing of financial instruments is crucial for its own risk management. In both cases, an appropriate quantification of the risks necessitates the use of complex mathematical tools and models. The proposed research aims at analyzing such mathematical models. An insurer must retain sufficient capital to meet its financial obligations while interacting with shareholders and tax authorities. That is, an event such as 'ruin' must be taken care of, in order to ensure that the insurer remains solvent, while dividend and tax payments have to be made. Our research aims at analyzing fairly general insurance risk processes where such features would be included. Outcomes from the first part of this research project will provide new and more powerful quantitative tools to insurers. On the other hand, a financial institution should be able to price accurately the financial instruments that it buys and sells. While most theoretical models are built using the concept of 'continuity', the reality in practice is 'discrete' and thus, for the company to be able to implement the models using computers, discretization analysis must be pursued. The second part of this research focuses on the development of discretization techniques to simulate and analyze stock prices and interest rates. These are typically modelled with continuous dynamics and we are planning to provide approximating methods of these quantities. It is hoped that our tools will be included in the toolbox of practitioners.