Quantitative measure of risk is a key element in risk management for many financial institutions and regulatory authorities.
Over the past few decades, many risk measures have been introduced. In all of these research, it is assumed that the information on decision maker’s risk preference is complete.
In this project, we propose to study robust mechanisms for quantitative risk measurement and management where decision maker’s risk preference is ambiguous. We focus on the distortion risk measure which allows us to use a distortion functional to characterize a decision maker’s risk preference and construct the ambiguity set in the absence of complete information of the true preference.
We propose to develop effective elicitation procedures to construct the ambiguity set and numerical schemes for computing the robust risk measure.
As an application, we apply the proposed robust models to capital allocation problems. This research fills out an important gap in the area of risk measurement and risk management and will have some direct and/or indirect impact on behavioural economics.