文档介绍：Finance Stochast. 3, 345–369 (1999)
c Springer-Verlag 1999
Bounds on prices of contingent claims
in an intertemporal economy with proportional
transaction costs and general preferences
e M. Constantinides1,2,?, Thaleia Zariphopoulou3,??
1 Graduate School of Business, The University of Chicago, 1101 East 58th Street, Chicago, IL 60637,
USA (e-mail: ******@)
2 The National Bureau of Economic Research, 1050 Massachusetts Avenue, Cambridge, MA 02138,
USA
3 School of Business and Department of Mathematics, University of Wisconsin, Madison, WI 53706,
USA
Abstract. Analytic bounds on the reservation write price of European-style con-
tingent claims are derived in the presence of proportional transaction costs in
a model which allows for intermediate trading. The option prices are obtained
via a utility maximization approach paring the maximized utilities with
and without the contingent claim. The mathematical e mainly from the
theories of singular stochastic control and viscosity solutions of nonlinear partial
differential equations.
Key words: Contingent claim prices, bounds on prices, transaction costs, vis-
cosity solutions
JEL classification: C6, D9, G1
Mathematics Subject Classification (1991): 93E20, 60G40
1. Introduction
In a frictionless market Black and Scholes (1973) and Merton (1973) relied on an
ingenious no-arbitrage argument to price an option on a stock when the interest
rate is constant and the stock price follows a geometric Brownian process. They
presented a self-financing, dynamic trading policy between the bond and stock
accounts which replicates the payoff of the option. They then argued that absence
of arbitrage dictates that the option price is equal to the cost of setting up the
? e Constantinides acknowledges partial financial support from the Center for Research in
Security Prices, the University of Chicago.
?? Thaleia Zariphopoulou acknowledges partial support from the Alfre