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Duplicating Contingent Claims by the Lagrange Method

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  • Gregory C. Chow

    (Princeton University)

Abstract

The problem of investing y(0) dollars at time 0 to duplicate a contigent claim is formulated as a dynamic optimization problem and solved by the Langrange method. If the function defining dy(t) is concave in y(t), owing to costs of trading in incomplete markets, there is an economy of scale in producing many claims simultaneously, thus explaining the profitability of institutions in providing such financial services.

Suggested Citation

  • Gregory C. Chow, 2003. "Duplicating Contingent Claims by the Lagrange Method," Finance 0306004, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0306004
    Note: Published in Pacific Economic Review, 4:3 (1999)
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    References listed on IDEAS

    as
    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    3. Chow, Gregory C., 1997. "Dynamic Economics: Optimization by the Lagrange Method," OUP Catalogue, Oxford University Press, number 9780195101928.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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    Finance;

    JEL classification:

    • G - Financial Economics

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