论文标题
连续时间单调均值变化投资组合在跳跃模型中选择
Continuous-Time Monotone Mean-Variance Portfolio Selection in Jump-Diffusion Model
论文作者
论文摘要
我们在跳跃模型中研究单调均值变化（MMV）偏好下的连续时间投资组合选择，并在动态设置中首次提供了与经典均值（MV）偏好下的明确解决方案。我们证明，计算MMV偏好的潜在度量可能仅限于非负Doléans-Dade指数。我们发现，当跳跃尺寸大于风险市场价格的倒数时，MMV可以解决MV的非单调性和自由现金流问题。这种结果与Dybvig和Ingersoll的最早结果完全可比。从经济上讲，我们表明，MMV的本质在于定价运营商始终保持非负值，当跳跃超过一定阈值时，分配的价值为零，避免了非单调性问题。结果，MMV投资者的行为与MV投资者明显不同。此外，我们验证了两资金分离，并为MMV投资者建立单调资本资产定价模型（单调CAPM）。我们还在约束交易模型中研究MMV，并提供三个特定的数值示例，以显示MMV的效率。我们的发现可以成为MMV和Monotone CAPM有效性的未来经验测试的至关重要的理论基础。
We study continuous-time portfolio selection under monotone mean-variance (MMV) preferences in a jump-diffusion model, presenting an explicit solution different from that under classical mean-variance (MV) preferences in dynamic settings for the first time. We prove that the potential measures calculating MMV preferences can be restricted to non-negative Doléans-Dade exponentials. We find that MMV can resolve the non-monotonicity and free cash flow stream problems of MV when the jump size can be larger than the inverse of the market price of risk. Such result is completely comparable to the earliest result by Dybvig and Ingersoll. Economically, we show that the essence of MMV lies in the pricing operator always remaining non-negative, with a value of zero assigned when the jump exceeds a certain threshold, avoiding the issue of non-monotonicity. As a result, MMV investors behave markedly different from MV investors. Furthermore, we validate the two-fund separation and establish the monotone capital asset pricing model (monotone CAPM) for MMV investors. We also study MMV in a constrained trading model and provide three specific numerical examples to show MMV's efficiency. Our finding can serve as a crucial theoretical foundation for future empirical tests of MMV and monotone CAPM's effectiveness.
