Robust No Arbitrage and the Solvability of Vector-Valued Utility Maximization Problems
9 Pages Posted: 6 Sep 2019
Date Written: August 21, 2019
A market model with d assets in discrete time is considered where trades are subject to proportional transaction costs given via bid-ask spreads, while the existence of a numeraire is not assumed. It is shown that robust no arbitrage holds if, and only if, there exists a Pareto solution for some vector-valued utility maximization problem with component-wise utility functions. Moreover, it is demonstrated that a consistent price process can be constructed from the Pareto maximizer.
Keywords: Bid-ask spread, robust no arbitrage, Pareto maximizer, utility maximization, consistent price process
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