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On infinite-horizon minimum-cost hedging under cone constraints

  • Kevin Huang

We prove there exists and analyze a strategy that minimizes the cost of hedging a liability stream in infinite-horizon incomplete security markets with a type of constraints that feasible portfolio strategies form a convex cone. We provide a theorem that extends Stiemke Lemma to over cone domains and we use the result to construct a series of primal-dual problems. Applying stochastic duality theory, dynamic programming technique and the theory of convex analysis to the dual formulation, we decompose the infinite-horizon dynamic hedging problem into one-period static hedging problems such that optimal portfolios in different events can be solved for independently.

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Paper provided by Utah State University, Department of Economics in its series Working Papers with number 2000-22.

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Length: 21 pages
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Handle: RePEc:usu:wpaper:2000-22
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  1. Aliprantis, C. D. & Brown, D. J. & Werner, J., 2000. "Minimum-cost portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1703-1719, October.
  2. Kevin X.D. Huang & Jan Werner, 2000. "Asset price bubbles in Arrow-Debreu and sequential equilibrium," Economic Theory, Springer, vol. 15(2), pages 253-278.
  3. Marsh, Paul, 1982. " The Choice between Equity and Debt: An Empirical Study," Journal of Finance, American Finance Association, vol. 37(1), pages 121-44, March.
  4. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
  5. 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.
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  7. Constantinides, George M, 1986. "Capital Market Equilibrium with Transaction Costs," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 842-62, August.
  8. Kevin Huang, . "Valuation and asset pricing in infinite-horizon sequential markets with portfolio constraints," Working Papers 2000-09, Utah State University, Department of Economics.
  9. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
  10. Taggart, Robert A, Jr, 1977. "A Model of Corporate Financing Decisions," Journal of Finance, American Finance Association, vol. 32(5), pages 1467-84, December.
  11. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
  12. Robert J. Shiller, 1992. "Measuring Asset Values for Cash Settlement in Derivative Markets: Hedonic Repeated Measures Indices and Perpetual Futures," Cowles Foundation Discussion Papers 1036, Cowles Foundation for Research in Economics, Yale University.
  13. Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
  14. Edirisinghe, Chanaka & Naik, Vasanttilak & Uppal, Raman, 1993. "Optimal Replication of Options with Transactions Costs and Trading Restrictions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(01), pages 117-138, March.
  15. Luttmer, Erzo G J, 1996. "Asset Pricing in Economies with Frictions," Econometrica, Econometric Society, vol. 64(6), pages 1439-67, November.
  16. Broadie, Mark & Cvitanic, Jaksa & Soner, H Mete, 1998. "Optimal Replication of Contingent Claims under Portfolio Constraints," Review of Financial Studies, Society for Financial Studies, vol. 11(1), pages 59-79.
  17. Bernard Bensaid & Jean-Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86.
  18. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  19. Naik, Vasanttilak & Uppal, Raman, 1994. "Leverage Constraints and the Optimal Hedging of Stock and Bond Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(02), pages 199-222, June.
  20. Dumas, Bernard & Luciano, Elisa, 1991. " An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-95, June.
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