Minimal Cost Index Tracking Under Nonlinear Transaction Costs and Minimal Transaction Unit Constraints

Abstract

Index tracking is a very common and popular approach in portfolio management. When there is neither (nonconvex) transaction costs nor minimal transaction unit constraints, the problem can be formulated as a convex least square problem, so that it can be solved by standard methods. However, when the transaction cost is nonconvex and not negligible, or if there is a minimal unit constraint on the amount of transaction, the problem becomes a nonconvex minimization problem with discrete variables. In this paper, we will propose a branch and bound algorithm for solving this class of problems and show that it can solve an index tracking problem of practical size in a reasonable amount of computation time.

Robust portfolio optimization with a hybrid heuristic algorithm

“…The right graph shows box plots of transformed empirical distribution functions for all numbers of function evaluations. For the box plots each function value is transformed into the percentage by which it is worse than the optimal solution obtained by CPLEX Note that a problem like (2) can be formulated as a small/medium size mixed integer quadratic programming problem (MIQP), when using linearization techniques (see, e.g., Konno and Wijayanayake 2001;Guastaroba et al 2009). MIQP problems can be solved to optimality with a general purpose solver (e.g.…”

Economic design of water distribution systems in buildings

“…A global optimal solution of the program NLP may be found by using a branch-andbound algorithm based on a decomposition of the feasible set of the program, similar to that described in Horst et al (2000); Horst and Tuy (1993); Konno and Wijayanayake (2001). This procedure exploits a binary tree, where each node is associated to a Nonlinear Program of the form .…”

“…As is discussed in Konno and Wijayanayake (2001), for this method to be efficient, techniques for finding lower and upper bounds have to be developed. If for a given node the current lower bound was greater than or equal to the best upper bound, then there is no need to search from this node.…”

“…The variable for branching the tree from the node previously chosen is chosen using an adaptation of the heuristic rule presented in Konno and Wijayanayake (2001). Let x * * = (x * * k ) k = 1,2,..., n ∈ R n be an optimal solution of the program NLP(node), associated with the current node.…”

Rebalance Schedule Optimization of a Large Scale Portfolio Under Transaction Cost

“…Fbr example, in Konno and Wijayanayake [9], they considered a rebalancing portfolio optimization problem with concave transaction cost functions and they proposed a branch and bound algorithm to solve this problem. In Konno and Yamamoto [11] [10].…”