This paper deals with the solution concepts,scalarization and existence of solutions formultiobjective generalized game. The scalarization method used in this paper can characterizecompletely the solutions and be appl...This paper deals with the solution concepts,scalarization and existence of solutions formultiobjective generalized game. The scalarization method used in this paper can characterizecompletely the solutions and be applied to prove the existence of solutions for quasi-convexmultiobjective generalized game. On the other hand,a new concept of security strategy isintroduced and its existence is proved.At last,some relations between these solutions areestablished.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This paper deals with the solution concepts,scalarization and existence of solutions formultiobjective generalized game. The scalarization method used in this paper can characterizecompletely the solutions and be applied to prove the existence of solutions for quasi-convexmultiobjective generalized game. On the other hand,a new concept of security strategy isintroduced and its existence is proved.At last,some relations between these solutions areestablished.
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.
