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AN ARBITRAGE INTERPRETATION OF CLASSICAL OPTIMIZATION
Author(s) -
Ellerman David P.
Publication year - 1990
Publication title -
metroeconomica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.256
H-Index - 29
eISSN - 1467-999X
pISSN - 0026-1386
DOI - 10.1111/j.1467-999x.1990.tb00469.x
Subject(s) - arbitrage , lagrange multiplier , multiplicative function , economics , mathematical economics , heuristic , interpretation (philosophy) , order (exchange) , mathematics , mathematical optimization , financial economics , computer science , finance , mathematical analysis , programming language
The paper mathematically develops the heuristic idea that the first‐order necessary conditions for a classical constrained optimization problem are equivalent to a market being arbitrage‐free ‐ with the Lagrange multipliers being the arbitrage‐free market prices. The arbitrage notions start with the multiplicative Kirchhoff's Voltage Law and then generalize to matrix algebra. The basic result shows the normalized arbitrage‐free «market prices» (the Lagrange multipliers) resulting from a classical constrained optimizaton problem can always be obtained as a ratio of cofactors. The machinery also gives an economic interpretation of Cramer's Rule as a competitive equilibrium condition.