185 spring 2004

Utility-Based Valuation of Risk

We can derive a value for risk from the curvature of an agent's utility function. There are three possible curvatures.

While the log function is a popular choice and it does occupy an interesting niche in the derivatives of polynomials, it requires a fancier calculator and does not work well with an outcome of $0. We will, therefore, use square root utility.

We reviewed the notion of expected value, which is important because the sample mean converges to the expected value in large samples.

An example that shows how we make this connection:

We deriive a value for risk by assuming that agents care about expected utility, not expected dollars.