The balance space approach in optimization with Riesz spaces valued objectives. An application to financial markets

The balance set approach, first introduced in [1, pp. 138–140], is developed for optimization problems with objective functions taking values in n. As pointed out in [2,3], balance points have important economical interpretations. Since the theory of Riesz spaces and Banach lattices become more and more the natural setting for general equilibrium and dynamic economic models, see for instance [4], we propose here an extension of the balance space approach of [3], to models with objective functions taking values in Riesz spaces. As an application, we present an optimization problem with an objective function valued in an L2-space. It describes the process of an agent maximizing the profit coming from an arbitrage portfolio in a financial market.