Dynamic risk measurement, with an application to a pension fund setting

The financial crisis has highlighted that economic agents have notbeen successful in associating capital requirements with the risks undertaken by financial institutions. The connection between capitalrequirements and risk-taking has to be improved. This thesis focuseson the improvement of risk measurement. First, we provide a literaturereview on static and dynamic convex measures of risk. An explicitconvex measure of risk is given by the entropic risk measure. We studythis risk measure and its connection with stochastic differential equations.As an extension to the entropic risk measure, we also investigatea risk measure that allows for some degree of ambiguity in choosing aprobabilistic model of some random variable. The literature has oftenfocused on risk measurement for random variables. To take into accountthe dynamic fluctuation of intermediate cash flows, we developan entropic risk measure for random processes. Finally, we apply somemeasures of risk to a pension fund setting.