Capital Asset Pricing Method Based on ε-Hedging Strategy

By defining e-hedging strategy, applying duality principle of linear programming and martingale measure theory, we present a kind of calculation method for the seller's arbitrage price and the buyer's arbitrage price of capital asset in finite (state) security market. We study the following two cases: (a) allowing short selling securities, and allowing borrowing and lending cash; (b) not allowing short selling securities, but allowing borrowing and lending cash. The analyses show that the e-arbitrage prices and the bid-ask price interval of the capital asset can be obtained by solving corresponding linear programming problems in martingale measure's spaces or super-martingale spaces corresponding to the securities. In the end, we discuss the cases in which the investor is risk-averse, risk-prone or risk-neutral.