In this paper we ask whether  arbitrage-free prices are obtained by utility maximization. This is found to be true for any given investor , provided that one considers the marginal utility-based prices relative to all initial endowments with finite utility  .
In this paper we ask whether , given a stock market and an illiquid derivative, there exists arbitrage-free prices at which an 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 .
A
, given a stock market and an illiquid derivative, there exists
R
are obtained by utility maximization. This is found to be true
at which an 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
R
, provided that one considers the marginal utility-based prices relative to
if one considers
A
, 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