Shou-Yang Wang

Optimal Portfolio Selection of Assets with Transaction Costs and No Short Sales

In the real financial markets, any movement of money between assets incurs a transaction cost proportional to the size of the transaction, paid from the bank account. In most cases, investors or portfolio managers usually start with an existing portfolio and make decisions of adjustment, probably, due to the changes of information about these securities. Since the revision entails both purchases and sales of securities that both incur transaction costs, the transaction cost is a V-shaped function of the difference between a new portfolio and the existing one. Obviously, the transaction cost has a direct impact on one’s investment performance, So, transaction costs have rightly become an important factor of concern and frustration for investors. The net return of a portfolio of securities should be evaluated by taking the costs into consideration. Arnott and Wagner (1990) observed that ignoring the transaction costs might result in inefficient portfolios. The experimental analysis done by Yoshimoto (1996) also verifies this fact.

Connectedness of super efficient sets in vector optimization of set-valued maps

Abstract. This paper deals with the super efficient sets in vector optimization of set-valued maps. It is proved that these sets are connected under an assumption of cone-convexlikeness and upper semicontinuity.

On the existence and connectedness of solution sets of vector variational inequalities

Abstract. In this paper, we consider a more general form of weak vector variational inequalities and prove some results on the existence of solutions of our new class of weak vector variational inequalities in the setting of Hausdorff topological vector topological space. We also discuss the connectedness of a solution set to some vector variational inequalities, and obtain a useful sufficient condition.

SENSITIVITY ANALYSIS OF NONNEGATIVE IRREDUCIBLE MATRICES

Abstract We develop a method based on the additive perturbation of a nonnegative irreducible matrix to analyze its sensitivity. Bounds for the norm of the difference between the perturbed right eigenvector and the initial one, and bounds for the difference between the perturbed principal eigenvalue and the initial one are obtained without any additional assumption on the nonnegative irreducible matrix.

A minimax rule for portfolio selection in frictional markets

Abstract. In this paper, an optimal portfolio selection problem is formulated as a minimax problem in which tax and dividend are associated with transactions. The corresponding optimal portfolio is derived respectively in the market with and without riskless asset. Furthermore, the relation and main difference between this minimax principal and the classical M-V model as well as the existing two minimax models are discussed.

On Computation of Arbitrage for Markets with Friction

We are interested in computation of locating arbitrage in financial markets with frictions. We consider a model with a finite number of financial assets and a finite number of possible states of nature. We derive a negative result on computational complexity of arbitrage in the case when securities are traded in integer numbers of shares and with a maximum amount of shares that can be bought for a fixed price (as in reality). When these conditions are relaxed, we show that polynomial time algorithms can be obtained by applying linear programming techniques. We also establish the equivalence for no-arbitrage condition & optimal consumption portfolio.

Two types of duality in multiobjective fractional programming

In this paper, we tire concerned with duality of a multiobjective fractional program. Two different dual problems are introduced with respect to the primal multiobjective fractional program. Under a mild assumption, we prove a weak duality theorem and a strong duality theorem for each type of duality. Finally, we explore some relations between these two types of duality.

A MINIMAX INEQUALITY FOR VECTOR-VALUED MAPPINGS

Abstract This paper presents a minimax inequality for vector-valued mappings in Hausdorff topological vector spaces with pointed closed convex cones.

5-STRICTLY QUASI-CONCAVE VECTOR MAXIMISATION

In this paper, we discuss the relationship among the concepts of an 5-strictly quasiconcave vector-valued function introduced by Benson and Sun, a C-strongly quasiconcave vector-valued function and a C-strictly quasiconcave vector-valued function in a topological vector space with a lattice ordering. We generalise a main result obtained by Benson and Sun about the closedness of an efficient solution set in multiple objective programming. We prove that an efficient solution set is closed and connected when the objective function is a continuous 5-strictly quasiconcave vectorvalued function, the objective space is a topological vector lattice and the ordering cone has a nonempty interior.

Two theorems on multilevel programming problems with dominated objective functions

In this paper, we present two theorems on the structure of a type of multilevel programming problems. The theorems explore relations among a multilevel programming problem, a dynamical programming, and a nonlinear programming problem.