We study the set of Davis (marginal utility-based) prices of a financial derivative in the case where the investor has a non-replicable random endowment. We give a new characterisation of the set of all such prices, and provide an example showing that even in the simplest of settings – such as Samuelson’s geometric Brownian motion model –, the interval of Davis prices is often a non-degenerate subinterval of the set of all no-arbitrage prices. This is in stark contrast to the case with a constant or replicable endowment where non-uniqueness of Davis prices is exceptional. We provide formulas for the endpoints of these intervals and illustrate the theory with several examples.

中文翻译：

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戴维斯有条件定价

在投资者拥有不可复制的随机end赋的情况下，我们研究了金融衍生品的戴维斯（基于边际效用）价格集。我们对所有这些价格的集合进行了新的描述，并提供了一个示例，表明即使在最简单的设置（例如Samuelson的几何布朗运动模型）中，戴维斯价格的区间也常常是集合的非退化子间隔所有无套利价格。这与end赋恒定或可复制的情况形成鲜明对比，在这种情况下，戴维斯价格的非唯一性是例外。我们为这些区间的端点提供公式，并通过几个示例来说明该理论。