Existence and Uniqueness for the Multivariate Discrete Terminal Wealth Relative

Abstract

In this paper, the multivariate fractional trading ansatz of money management from Vince (Vince 1990) is discussed. In particular, we prove existence and uniqueness of an “optimal f” of the respective optimization problem under reasonable assumptions on the trade return matrix. This result generalizes a similar result for the univariate fractional trading ansatz. Furthermore, our result guarantees that the multivariate optimal f solutions can always be found numerically by steepest ascent methods.

Keywords

• fractional trading
• optimal f
• multivariate discrete terminal wealth relative
• risk and money management
• portfolio theory