风险约束下的增长率最大化
Maximizing the Growth Rate under Risk Constraints
摘要：
本文在不完全伊藤过程金融市场模型的背景下研究了一类风险约束下增长率最大化的遍历问题。包括{ \em风险价值}（VaR）、{ \em风险尾部价值}（TVaR）和{ \em有限预期损失}（LEL）在内，这些约束既可以是财富相关的（相对的），也可以是财富无关的（绝对的）。最优策略存在于一个适当的容许类中，并且可以通过统一的、状态相关的无约束（Merton）最优投资组合的缩减来明确地获得。这意味着风险约束的财富增长优化器在局部表现得像CRRA投资者，相对风险规避系数取决于市场系数的当前值。
英文摘要：
We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, Itô-process models of financial markets with random ergodic coefficients. Including {\em value-at-risk} (VaR), {\em tail-value-at-risk} (TVaR), and {\em limited expected loss} (LEL), these constraints can be both wealth-dependent(relative) and wealth-independent (absolute). The optimal policy is shown to exist in an appropriate admissibility class, and can be obtained explicitly by uniform, state-dependent scaling down of the unconstrained (Merton) optimal portfolio. This implies that the risk-constrained wealth-growth optimizer locally behaves like a CRRA-investor, with the relative risk-aversion coefficient depending on the current values of the market coefficients.
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