Department of Mathematics
Multistage Portfolio Optimization: A Duality Result in Conic Market Models
- Author(s): Bassett, Robert
- Le, Khoa
- et al.
Published Web Locationhttps://arxiv.org/pdf/1601.00712.pdf
We prove a general duality result for multi-stage portfolio optimization problems in markets with proportional transaction costs. The financial market is described by Kabanov's model of foreign exchange markets over a finite probability space and finite-horizon discrete time steps. This framework allows us to compare vector-valued portfolios under a partial ordering, so that our model does not require liquidation into some numeraire at terminal time. We embed the vector-valued portfolio problem into the set-optimization framework, and generate a problem dual to portfolio optimization. Using recent results in the development of set optimization, we then show that a strong duality relationship holds between the problems.