The aim of this paper is to provide several examples of convex risk measures necessary for the application of the … classical portfolio risk measures such as the standard deviation, we, in particular, construct risk measures related to the … and Mahmoud (2017), and Zabarankin, Pavlikov, and Uryasev (2014), who used the absolute drawdown, our risk measure is …

Utility and risk are two often competing measurements on the investment success. We show that efficient trade … of utility and risk. This is a rather general pattern. The modern portfolio theory of Markowitz (1959) and the capital … market pricing model Sharpe (1964), are special cases of our general framework when the risk measure is taken to be the …

market model; (b) trading strategies; (c) risk and utility functions (performance criteria); and (d) the optimization problem … fraction). As application, we discuss the utility function of compounded return and the risk measure of relative log drawdowns. …