论文标题
关于最佳投资和随机占主导地位的价值函数的分析性
On the analyticity of the value function in optimal investment and stochastically dominant markets
论文作者
论文摘要
我们研究了最佳投资中价值函数的分析性，并通过最终财富的预期效用以及与随机占主导地位的财务模型的关系。我们确定了一类公用事业和一类我们建立分析性的半木制模型。具体而言，这些实用程序具有完全单调的逆边缘，而市场模型在无限级随机主导地位的意义上具有最大元素。我们构建了两个反示例，本身是独立的，这表明如果实用程序或市场模型不属于各自的特殊类别，则分析性会失败。我们还为价值函数及其优化者的衍生物，所有订单的衍生物提供明确的公式。最后，我们表明，对于一组超级智能屈曲者，无限顺序的随机优势等同于明显更强的二阶优势。
We study the analyticity of the value function in optimal investment with expected utility from terminal wealth and the relation to stochastically dominant financial models. We identify both a class of utilities and a class of semi-martingale models for which we establish analyticity. Specifically, these utilities have completely monotonic inverse marginals, while the market models have a maximal element in the sense of infinite-order stochastic dominance. We construct two counterexamples, themselves of independent interest, which show that analyticity fails if either the utility or the market model does not belong to the respective special class. We also provide explicit formulas for the derivatives, of all orders, of the value functions as well as their optimizers. Finally, we show that for the set of supermartingale deflators, stochastic dominance of infinite order is equivalent to the apparently stronger dominance of second order.
