Our paper contributes to the literature by extending the theory of the mean-variance (MV) rules for both risk averters and risk lovers to the MV rule for investors with reverse S-shaped utility. To do so, we first introduce the definition of the MV rule for investors with reverse S-shaped...

In this paper, we first develop some properties to state the relationships among central moments, stochastic dominance (SD), risk-seeking stochastic dominance (RSD), and integrals for the general utility functions and the polynomial utility functions of both risk averters and risk seekers. We...

In this paper, we will investigate whether there is any Sharpe ratio rule or Omega ratio rule that can be used to show that one asset outperforms another asset if it has a higher Sharpe ratio and/or Omega ratio. We find that Sharpe ratio rule could not detect preference of both risk averters and...

Mathematics plays a vital role in many areas of finance and provides the theories and tools that have been widely used in all areas of finance. In this editorial, we tell authors the ideas on what types of papers we will accept for publication in the area of mathematical finance. We will discuss...