DO ARBITRAGE‐FREE PRICES COME FROM UTILITY MAXIMIZATION?
DO ARBITRAGE‐FREE PRICES COME FROM UTILITY MAXIMIZATION?
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无套利价格来自效用最大化吗？
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Pietro Siorpaes
中科院分区：
文献类型：
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作者：
Pietro Siorpaes
在本文中，我们要问的是，给定一个股票市场和一个非流动性衍生品，是否存在无套利价格，在这个价格上，效用最大化的代理人总是想购买衍生品，而不管他自己的衍生品和现金的初始禀赋如何。我们证明，这是假的任何给定的投资者，如果一个考虑所有的初始禀赋有限的效用，它可以是真的，如果一个限制在内部的禀赋。然而，我们展示了边界上的禀赋如何引起非常奇怪的现象;例如，具有这种禀赋的投资者即使在任意接近某个套利价格的价格下也会选择不交易衍生品。
In this paper we ask whether, given a stock market and an illiquid derivative, there exists arbitrage‐free prices at which a utility‐maximizing agent would always want to buy the derivative, irrespectively of his own initial endowment of derivatives and cash. We prove that this is false for any given investor if one considers all initial endowments with finite utility, and that it can instead be true if one restricts to the endowments in the interior. We show, however, how the endowments on the boundary can give rise to very odd phenomena; for example, an investor with such an endowment would choose not to trade in the derivative even at prices arbitrarily close to some arbitrage price.