Duplicating Contingent Claims by the Lagrange Method
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.
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- 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.
- Chow, Gregory C., 1997. "Dynamic Economics: Optimization by the Lagrange Method," OUP Catalogue, Oxford University Press, number 9780195101928.
- 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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