Quadratic Hedging Principles

Abstract

Fix a future time T and let L be the value of a liability at that time. One example of L is the portfolio value of derivative instruments issued by a bank. Another example is the value of future claims from insurance products sold by an insurance company. Typically the holder of the liability does not want to speculate on a favorable outcome of this random variable. The ideal approach to managing the risk of an unfavorable outcome of L would be to purchase a portfolio whose value A (A for assets) at the future time T exactly matches that of the liability. In that case, A = L, and the risk of an unfavorable outcome of L is removed completely by purchasing the asset portfolio. The problem with this approach is that it is not always possible to find a portfolio of assets whose future value corresponds exactly to that of the liability; one example is when the liability is made up of insurance claims.