Most decision making processes involve risk associated with the uncertainty of a range of outcomes that may, or may not, occur at some time in the future. In recent years, many of the recent advances in risk theory have come from the field of financial mathematics. While the latter subject is now well developed I claim that there are still some important aspects of decision-making involving risk that are not covered by the existing theory. In particular, I believe that the following three questions require further investigations. 1. How to ma…