Author(s)

David L. Stowe

Department of Finance, Ohio University, Athens, Ohio, USA.

This paper explores the mathematics behind optimal portfolio construction when relative utility and risk are considered together in a general sense. I derive the portfolio optimization problems when subject to both a general liner constraint and a constraint to tracking error (a quadratic constraint), the most pervasive constraint placed on delegated portfolio managers. This unifies three very influential papers from the evolution of optimal portfolio theory. In addition, I also analyze the general linear constraint when applied to Sharpe Ratio maximization. When applied together, these formulations can allow principals and agents to better analyze alternatives and negotiate contracting in order to ensure that the constraints generate proper utility maximization.

Portfolio Mathematics, Optimization, Delegated Portfolio Management, Tracking Error, Utility Maximization

Stowe, D. (2019) Portfolio Mathematics with General Linear and Quadratic Constraints. Journal of Mathematical Finance, 9, 675-690. doi: 10.4236/jmf.2019.94034.