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On infinite-horizon minimum-cost hedging under cone constraints

Author

Listed:
  • 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: https://repec.bus.usu.edu/RePEc/usu/pdf/ERI2000-22.pdf
    File Function: First version, 2000
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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. Araujo, Aloisio & Chateauneuf, Alain & Faro, José Heleno, 2018. "Financial market structures revealed by pricing rules: Efficient complete markets are prevalent," Journal of Economic Theory, Elsevier, vol. 173(C), pages 257-288.

    More about this item

    Keywords

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    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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