Risk measures and optimal portfolio selection
研究了凹扭曲风险度量的性质，并提出了在随机回报环境下为未来确定性支付确定准备金的方法，包括基于共单调风险理论的近似和最优投资策略。
We investigate the class of (concave) distortion risk measures and give an overview of many tractable properties of this class. Further, we consider the problem of determining an adequate provision for a series of future deterministic payments, in a stochastic return environment. The provision is determined as a risk measure (VaR or TailVaR e.g.) for the random variable representing the stochastically discounted value of these future payments. Several approximations, based on the theory of comonotonic risks, are proposed. We also consider the problem of determining the provision for a series of future deterministic payments in a situation where several investment possibilities are available. We determine optimal investment strategies in the class of continuously rebalanced portfolios. Optimality is defined in terms of optimal values for a given risk measure of the present value random variable. Finally, we determine optimal investment strategies for final wealth problems, where deterministic future savings are performed in order to reach a target capital at some deterministic future date.