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On infinite-horizon minimum-cost hedging under cone constraints

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  • Kevin Huang

Abstract

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.

Suggested Citation

  • Kevin Huang, "undated". "On infinite-horizon minimum-cost hedging under cone constraints," Working Papers 2000-22, Utah State University, Department of Economics.
  • Handle: RePEc:usu:wpaper:2000-22
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    File URL: ftp://repec.bus.usu.edu/RePEc/usu/pdf/ERI2000-22.pdf
    File Function: First version, 2000
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    References listed on IDEAS

    as
    1. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
    2. 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.
    3. 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.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. repec:dau:papers:123456789/5630 is not listed on IDEAS
    7. Shiller, Robert J, 1993. " Measuring Asset Values for Cash Settlement in Derivative Markets: Hedonic Repeated Measures Indices and Perpetual Futures," Journal of Finance, American Finance Association, vol. 48(3), pages 911-931, July.
    8. Kevin Huang, "undated". "Valuation and asset pricing in infinite-horizon sequential markets with portfolio constraints," Working Papers 2000-09, Utah State University, Department of Economics.
    9. 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.
    10. Marsh, Paul, 1982. " The Choice between Equity and Debt: An Empirical Study," Journal of Finance, American Finance Association, vol. 37(1), pages 121-144, March.
    11. Kevin X.D. Huang & Jan Werner, 2000. "Asset price bubbles in Arrow-Debreu and sequential equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 253-278.
    12. Taggart, Robert A, Jr, 1977. "A Model of Corporate Financing Decisions," Journal of Finance, American Finance Association, vol. 32(5), pages 1467-1484, December.
    13. George M. Constantinides, 2005. "Capital Market Equilibrium with Transaction Costs," World Scientific Book Chapters,in: Theory Of Valuation, chapter 7, pages 207-227 World Scientific Publishing Co. Pte. Ltd..
    14. 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.
    15. Luttmer, Erzo G J, 1996. "Asset Pricing in Economies with Frictions," Econometrica, Econometric Society, vol. 64(6), pages 1439-1467, November.
    16. 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 577-595, June.
    17. 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.
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    19. 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 637-654, May-June.
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    Cited by:

    1. Bidian, Florin, 2015. "Portfolio constraints, differences in beliefs and bubbles," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 317-326.
    2. Chen, Yingshan & Dai, Min & Xu, Jing & Xu, Mingyu, 2015. "Superhedging under ratio constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 250-264.
    3. Baccara, Mariagiovanna & Battauz, Anna & Ortu, Fulvio, 2006. "Effective securities in arbitrage-free markets with bid-ask spreads at liquidation: a linear programming characterization," Journal of Economic Dynamics and Control, Elsevier, vol. 30(1), pages 55-79, January.
    4. repec:eee:jetheo:v:173:y:2018:i:c:p:257-288 is not listed on IDEAS

    More about this item

    Keywords

    Infinite horizon; minimum-cost hedging; cone constraints;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

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