基于随机基准的三基金定理动态决策模型

The dynamic portfolio decision-making model with three-fund separation theorem based on stochastic benchmark

在Black-Scholes型金融市场下,通过一个随机过程来定义基准,以低于基准的不足概率作为风险约束,以最大化期望相对终端财富为决策目标,构建了动态投资组合决策模型,并给出了最优投资策略和有效前沿的显式表达式。结果表明:最优投资策略由无风险资产,修正的市场组合及“基准组合”构成,可视为三基金定理。最后给出了数值例子。

Under the Black-Scholes type financial market, a dynamic portfolio decision-making model is proposed, where the expected relative terminal wealth is maximized under aconstraint on the shortfall probability below a benchmark defined by a stochastic process. Stochastic analysis method and nonlinear programming theory are applied to obtain the explicit solutions of the optimal strategies and the efficient frontiers. The results exhibit three-fund separation theorem which include the riskless asset, revised market portfolio and benchmark portfolio. Numerical examples are presented.