Quantifiable, measurable risk is of critical importance when making data-driven decisions in finance and investment management, but what if the generally accepted practice of the investment industry for calculating risk possessed incorrect mathematical assumptions and embedded biases? This piece...

This paper originally proposes two unique closed-form solutions, respectively to risky assets only and a risk-free asset existing situations, of the mean-variance-skewness (MVS) optimization model subject to mean-sknewness-normalization constraints for portfolio selection. The efficient frontier...

Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two-dimensional space of utility and risk. This is a rather general pattern....

The aim of this paper is to provide several examples of convex risk measures necessary for the application of the general framework for portfolio theory of Maier-Paape and Zhu (2018), presented in Part I of this series. As an alternative to classical portfolio risk measures such as the standard...