Approximate utility

Philip Dybvig and Shu Li

Finance Research Letters, 2024, vol. 69, issue PA

Abstract: Approximating arbitrage or a perfect hedge in a limit implies approximation in utility (formally, expected utilities are continuous in L2), if and only if the utility function is bounded above and below by quadratics. We characterize when some special utility functions are continuous for all random consumptions with a common lower bound. Only linear, quadratic, and, in some cases, translated SAHARA utilities are continuous if there is no lower bound. We also characterize when a utility function defined on a convex subset can be extended to an L2-continuous nondecreasing and concave utility function on all of R.

Keywords: Approximate utility; Properness; von Neumann-Morgenstern; Quadratic utility (search for similar items in EconPapers)
JEL-codes: C0 D0 G0 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:finlet:v:69:y:2024:i:pa:s1544612324010729

DOI: 10.1016/j.frl.2024.106042

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