One index satisfies the duality axiom if one agent, who is uniformly more risk-averse than another, accepts a gamble, the latter accepts any less risky gamble under the index. Aumann and Serrano (2008) show that only one index defined for so-called gambles satisfies the duality and positive...

This paper studies a mean-risk portfolio choice problem for log-returns in a continuous-time, complete market. It is a growth-optimal portfolio choice problem under risk control. The risk of log-returns is measured by weighted Value-at-Risk (WVaR), which is a generalization of Value-at-Risk...

This paper analyzes the optimal investment policies of rank-dependent utility maximizing investor who must manage the risk exposure using a general law- invariant risk measure such as Value-at-Risk and tail Value-at-Risk. The analytic optimal solution is obtained via the so-called quantile...