Applications of General Equilibrium to Incomplete Markets and Finance

Purdue University, West Lafayette IN

Investigators

Abstract

The project is concerned with applications of the recent developments in general equilibrium theory to problems arising in incomplete markets and finance. When markets are not complete, an investor, who seeks portfolio insurance, will be interested in the cheapest hedge that is marketed. Such insurance will not exactly replicate the desired insured-payoff, but it is the "best'' that can be achieved using today's market. One of the proposed problems deals with several new methods of computing the minimum-cost portfolio by applying the newly developed portfolio dominance method. In another direction, a new incentive compatibility notion is proposed that will allow to develop a model where the standard accepted conditions in finance will guarantee that a security that can be obtained through incentive compatible trading must also allow all of its options (puts and calls) to be obtained through incentive compatible trading. Several applications in various disciplines of the techniques that are being developed in this project are planned. The most important of which seems to be on the problem of "Optimal Crop Diversification under Uncertainty" in agriculture. Crop diversification is still practiced widely by both small and large agricultural producers in industrialized countries. Smaller producers, especially vegetable producers, often find the fixed costs associated with crop specific technologies too high to be profitably employed. Large producers on the other hand usually find the use of specialized technology highly beneficial, yet they continue to plant different varieties or hybrids of the crop of specialization. Planting different varieties, often those that respond differently to uncontrollable elements of the local environment, provides farmers with a natural form of hedging against risk. The existing literature on risk in agriculture provides numerous insights into the proper role and use of crop insurance, price and revenue hedges, and weather related derivatives. Much of the discipline's existing literature and knowledge focuses on issues related to price uncertainty and methods to hedge against price risk. The proposed project will provide a complementary solution to these approaches by applying the method of minimum premium hedge to the crop diversification problem.