No-Arbitrage Bounds on Contingent Claims Prices with Convex Constraints on the Dollar Investments of the Hedge Portfolio
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.
|Date of creation:||17 Dec 1997|
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|Note:||Type of Document - LaTeX 2e; to print on PostScript; pages: 30 ; figures: included|
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- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Alain Bensoussan & Robert J. Elliott, 1995. "Attainable Claims In A Markov Market," Mathematical Finance, Wiley Blackwell, vol. 5(2), pages 121-131.
- Claus Munk, 1997. "Optimal Consumption/Investment Policies with Undiversifiable Income Risk and Borrowing Constraints," Finance 9712003, EconWPA.
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