Consider a risk-averse investor allocating a certain amount of capital w to n dependent risky assets, where the i-th asset will default if its stochastic return Xi is less than some predetermined threshold level li ≥ 0, for i = 1, … , n, and the investor wants to maximize the expected utility of the aggregate stochastic returns. In this paper, for assets with stochastic returns being left tail weakly stochastic arrangement increasing (LWSAI), the optimal and the worst allocation policies are derived as (0, … , 0, w) and (w, 0, … , 0), respectively. Some numerical examples are also provided to illustrate the theoretical fndings. These new results complement the corresponding ones in Cheung and Yang (Insur Math Econ 35:595–609, 2004) and Cai and Wei (J Multivar Anal 138:156–169, 2015), and partially answer the Open Problem 2 proposed in Li and Li (Quant Financ Econ 2(1):190–216, 2018).
