The Kuhn-Tucker conditions have been used to derive many significant results in economics. However, thus far, their derivation has been a little bit troublesome. The author directly derives the Kuhn-Tucker conditions ...The Kuhn-Tucker conditions have been used to derive many significant results in economics. However, thus far, their derivation has been a little bit troublesome. The author directly derives the Kuhn-Tucker conditions by applying a corollary of Farkas’s lemma under the Mangasarian-Fromovitz constraint qualification and shows the boundedness of Lagrange multipliers.展开更多
This paper extends Farkas Minkowski’s Lemma and Stiemke’s Lemma from the Euclidean space to (l 1,l ∞). The extensions of Farkas Minkowski’s Lemma and Stiemke’s Lemma are the Basic Valuation Theore...This paper extends Farkas Minkowski’s Lemma and Stiemke’s Lemma from the Euclidean space to (l 1,l ∞). The extensions of Farkas Minkowski’s Lemma and Stiemke’s Lemma are the Basic Valuation Theorem in the case (l 1,l ∞). The security price is weakly arbitrage free if and only if there exists a positive state vector; the security price is strictly arbitrage free if and only if there exists a strictly positive state vector. The present value of the securities prices at date 0 is the value of their returns over all countably infinite possible states of nature at date 1.展开更多
文摘The Kuhn-Tucker conditions have been used to derive many significant results in economics. However, thus far, their derivation has been a little bit troublesome. The author directly derives the Kuhn-Tucker conditions by applying a corollary of Farkas’s lemma under the Mangasarian-Fromovitz constraint qualification and shows the boundedness of Lagrange multipliers.
文摘This paper extends Farkas Minkowski’s Lemma and Stiemke’s Lemma from the Euclidean space to (l 1,l ∞). The extensions of Farkas Minkowski’s Lemma and Stiemke’s Lemma are the Basic Valuation Theorem in the case (l 1,l ∞). The security price is weakly arbitrage free if and only if there exists a positive state vector; the security price is strictly arbitrage free if and only if there exists a strictly positive state vector. The present value of the securities prices at date 0 is the value of their returns over all countably infinite possible states of nature at date 1.
