Duplicating Contingent Claims by the Lagrange Method
نویسنده
چکیده
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.
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