Abstract
We discuss the problem of pricing contingent claims, such as European call options, based on the fundamental principle of "absence of arbitrage" and in the presence of constraints on portfolio choice, for example, incomplete markets and markets with short-selling constraints. Under such constraints, we show that there exists an arbitrage-free interval which contains the celebrated Black-Scholes price (corresponding to the unconstrained case); no price in the interior of this interval permits arbitrage, but every price outside the interval does. In the case of convex constraints, the endpoints of this interval are characterized in terms of auxiliary stochastic control problems, in the manner of Cvitanić and Karatzas. These characterizations lead to explicit computations, or bounds, in several interesting cases. Furthermore, a unique fair price
Citation
I. Karatzas. S. G. Kou. "On the pricing of contingent claims under constraints." Ann. Appl. Probab. 6 (2) 321 - 369, May 1996. https://doi.org/10.1214/aoap/1034968135
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