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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.

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File URL: ftp://repec.bus.usu.edu/RePEc/usu/pdf/ERI2000-22.pdf
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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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Keywords: Infinite horizon; minimum-cost hedging; cone constraints;

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  1. 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 911-31, July.
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  8. 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.
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  16. repec:fth:inseep:9513 is not listed on IDEAS
  17. 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.
  18. 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.
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Cited by:
  1. 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.

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