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Abstract: For utility functions $u$ finite valued on $\mathbb{R}$, we prove a dualityformula for utility maximization with random endowment in generalsemimartingale incomplete markets. The main novelty of the paper is thatpossibly non locally bounded semimartingale price processes are allowed.Following Biagini and Frittelli \cite{BiaFri06}, the analysis is based on theduality between the Orlicz spaces $L^{\widehat{u}}, L^{\widehat{u}}^*$naturally associated to the utility function. This formulation enables severalkey properties of the indifference price $\piB$ of a claim $B$ satisfyingconditions weaker than those assumed in literature. In particular, theindifference price functional $\pi$ turns out to be, apart from a sign, aconvex risk measure on the Orlicz space $L^{\widehat{u}}$.



Author: Sara Biagini, Marco Frittelli, Matheus R. Grasselli

Source: https://arxiv.org/







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