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Duplicating Contingent Claims by the Lagrange Method
Author(s) -
Chow Gregory
Publication year - 1999
Publication title -
pacific economic review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.34
H-Index - 33
eISSN - 1468-0106
pISSN - 1361-374X
DOI - 10.1111/1468-0106.00078
Subject(s) - profitability index , economics , function (biology) , mathematical economics , lagrange multiplier , scale (ratio) , financial market , microeconomics , mathematics , mathematical optimization , finance , evolutionary biology , biology , physics , quantum mechanics
The problem of investing y (0) dollars at time 0 to duplicate a contingent claim is formulated as a dynamic optimization problem and solved by the Lagrange method. As an example, the well‐known formula of Black and Scholes on option pricing is derived. If the function defining dy ( t ) is concave in y ( t ), owing to costs of trading in incomplete markets, there is economy of scale in producing many claims simultaneously, thus explaining the profitability of institutions in providing such financial services.