scholarly journals A parametric simplex algorithm for linear vector optimization problems

2016 ◽  
Vol 163 (1-2) ◽  
pp. 213-242 ◽  
Author(s):  
Birgit Rudloff ◽  
Firdevs Ulus ◽  
Robert Vanderbei
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Simplex Algorithm ◽  
Vector Optimization Problems ◽  
Linear Vector ◽  
Linear Vector Optimization ◽  
Parametric Simplex Algorithm

scholarly journals AN ALGORITHM FOR CALCULATING THE SET OF SUPERHEDGING PORTFOLIOS IN MARKETS WITH TRANSACTION COSTS

2014 ◽  
Vol 17 (02) ◽  
pp. 1450012 ◽  
Author(s):  
ANDREAS LÖHNE ◽  
BIRGIT RUDLOFF
Keyword(s):  
Transaction Costs ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Market Model ◽  
Vector Optimization Problems ◽  
Explicit Calculation ◽  
Event Tree ◽  
Basket Options ◽  
Linear Vector ◽  
Linear Vector Optimization

We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs. The set of superhedging portfolios can be obtained by a recursive construction involving set operations, going backward in the event tree. We reformulate the problem as a sequence of linear vector optimization problems and solve it by adapting known algorithms. The corresponding superhedging strategy can be obtained going forward in the tree. Examples are given involving multiple correlated assets and basket options. Furthermore, we relate existing algorithms for the calculation of the scalar superhedging price to the set-valued algorithm by a recent duality theory for vector optimization problems. The main contribution of the paper is to establish the connection to linear vector optimization, which allows to solve numerically multi-asset superhedging problems under transaction costs.

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