Analytical solutions in risk management

In risk management, most traditional approaches are built around a fundamental desire for analytical tractability. The reason for this is obvious: with only minor computational power of computers the only way to guarantee quick solutions was through mathematics. And in practice, when risk assessment and portfolio optimization becomes part of your business, you wouldn’t want to have a model that needs hours or days in order to come up with some insights into your risks.

However, in reality the challenges on your analytical risk management model are rather high. It is almost sure that your model will not have to deal with one-dimensional risks only. Whether high-dimensionality arises through multiple assets or multi-period risk assessment of one asset only: both cases force you to deal with interactions of multiple random variables, thereby complicating an analytical solution enormously. And, of course: in most real world situations, you will encounter both cases. Life just ain’t easy…

In this post we will try to work out some circumstances that need to prevail in order that we could still hope to find an analytical solution. Still, whether such convenient circumstances also do occur in reality, is something that we will need to put some further thought on afterwards.