BFS 2002

Plenary Address

Optimal security design and diversification in financial markets with non-tradeable risks

Nicole El Karoui, Pauline Barrieu

We focus on the optimal characterization of a security based on a non-tradeable risk. On one hand, a bank is exposed to this particular risk and is willing to partly transfer this risk via a structured product. On the other hand, an investor is motivated by the diversification potential of such a security. Both agents have the opportunity to invest on the financial market through an optimal strategy that includes their respective global position. The bank's objective is then to determine the structure of the contract, maximizing its expected utility, where the price is given by the investor.
Based on an exponential utility criterion, the main result is that the optimal security is always proportional to the bank's exposure, and most importantly, is independent of any assumption on uncertainty, while the price is given by an indifference pricing rule.