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No-Arbitrage Bounds on Contingent Claims Prices with Convex Constraints on the Dollar Investments of the Hedge Portfolio

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  • Claus Munk

    (Odense University, Denmark)

Abstract

With constrained portfolios, contingent claims do not generally have a unique price, for which there are no arbitrage opportunities. We generalize earlier results of El Karoui and Quenez (1995) and Cvitanic and Karatzas (1993) by showing that there is an interval of no-arbitrage prices, when there are convex constraints on the dollar investments in the assets in the hedge portfolio. We also show that the bounds of the no-arbitrage interval can be found by solving two stochastic control problems, and we demonstrate how to solve these problems numerically.

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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 9712006.

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Length: 30 pages
Date of creation: 17 Dec 1997
Date of revision:
Handle: RePEc:wpa:wuwpfi:9712006

Note: Type of Document - LaTeX 2e; to print on PostScript; pages: 30 ; figures: included
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Web page: http://128.118.178.162

Related research

Keywords: Contingent claims pricing; constrained dollar investments; no- arbitrage bounds; numerical solution;

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  1. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  3. Hindy, Ayman & Huang, Chi-fu & Zhu, Steven H., 1997. "Numerical analysis of a free-boundary singular control problem in financial economics," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 297-327.
  4. Cuoco, Domenico, 1997. "Optimal Consumption and Equilibrium Prices with Portfolio Constraints and Stochastic Income," Journal of Economic Theory, Elsevier, vol. 72(1), pages 33-73, January.
  5. Harrison, J. Michael & Pliska, Stanley R., 1983. "A stochastic calculus model of continuous trading: Complete markets," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 313-316, August.
  6. Claus Munk, 1997. "Optimal Consumption/Investment Policies with Undiversifiable Income Risk and Borrowing Constraints," Finance 9712003, EconWPA.
  7. Alain Bensoussan & Robert J. Elliott, 1995. "Attainable Claims In A Markov Market," Mathematical Finance, Wiley Blackwell, vol. 5(2), pages 121-131.
  8. Rust, John, 1996. "Numerical dynamic programming in economics," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 14, pages 619-729 Elsevier.
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