Group for Research in Decision Analysis

Good Deals: Compatible Extension of Risk and Pricing Rules

Hirbod Assa

In this talk we consider a very simple hedging problem of minimizing a coherent risk measure subject to some constraint on the price. We will show that contrary to a similar hedging problem of maximizing an expected utility with the price constraint, this problem does not always have a solution. We will show that this problem has a solution if and only if Good Deals do not exist. A Good Deal is a financial position despite having negative risk costs nothing. We study these positions in some details and show how they are related to another yet known concept, incompatibility. At the end, we introduce some methods to modify the risk measure in order to remove Good Deals.