Upper and Lower Arbitrage Prices Under Portfolio Constraints: A Non-Classical Stochastic Control Approach

Dr. MH Chang

Department of Mathematical Sciences
University of Alabama in Huntsville

November 17, 2000

Abstract

In this talk, we consider the pricing of European options in a financial market with portfolio constraints. These constraints include shortselling, borrowing, or other restrictions. Contrary to the idealized Black-Scholes world, the constraints such as these often render the market incomplete in that the option cannot be exactly replicated. In this case, it is highly desirable to compute the upper (the lowest price the option seller can accept without risks) and the lower (the highest price the option buyer can afford to pay without risks) arbitrage prices. Based on an original dynamic programming principle, these problems can be formulated as two non-classical stochastic control problems. The upper and lower arbitrage prices can then be found by solving two variational inequalities in a weak (viscosity) sense.