论文标题
关于非偏见优化的风险和预期不足的风险措施之间的等价性
On the equivalence between Value-at-Risk- and Expected Shortfall-based risk measures in non-concave optimization
论文作者
论文摘要
我们研究了一个非共核优化问题，其中金融公司在基于风险的监管约束下最大程度地提高了盈余的预期效用。对于这个问题，我们考虑了四种不同的普遍风险限制（预期的不足，预期的折扣不足，价值风险和平均价值风险），并研究了它们对最佳解决方案的影响。我们的主要贡献是以最佳终端财富的形式获得了四个风险限制的分析解决方案。我们表明，这四个风险限制导致了相同的最佳解决方案，这与先前从相应的凹面优化问题获得的结论不同。与基准（不受约束的）非concave效用最大化问题相比，所有四个风险限制有效，等效地减少了零终端财富的集合，但不能完全消除这一集合，表明各个财务法规的成功和失败。
We study a non-concave optimization problem in which a financial company maximizes the expected utility of the surplus under a risk-based regulatory constraint. For this problem, we consider four different prevalent risk constraints (Expected Shortfall, Expected Discounted Shortfall, Value-at-Risk, and Average Value-at-Risk), and investigate their effects on the optimal solution. Our main contributions are in obtaining an analytical solution under each of the four risk constraints, in the form of the optimal terminal wealth. We show that the four risk constraints lead to the same optimal solution, which differs from previous conclusions obtained from the corresponding concave optimization problem under a risk constraint. Compared with the benchmark (unconstrained) non-concave utility maximization problem, all four risk constraints effectively and equivalently reduce the set of zero terminal wealth, but do not fully eliminate this set, indicating the success and failure of the respective financial regulations.
