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Dynamically consistent alpha‐maxmin expected utility
Author(s) -
Beissner Patrick,
Lin Qian,
Riedel Frank
Publication year - 2020
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12232
Subject(s) - knightian uncertainty , expected utility hypothesis , ambiguity , mathematical economics , economics , valuation (finance) , alpha (finance) , capital asset pricing model , infinitesimal , limit (mathematics) , arrow , econometrics , mathematical optimization , mathematics , computer science , finance , mathematical analysis , health care , cronbach's alpha , programming language , economic growth
The alpha‐maxmin model is a prominent example of preferences under Knightian uncertainty as it allows to distinguish ambiguity and ambiguity attitude. These preferences are dynamically inconsistent for nontrivial versions of alpha. In this paper, we derive a recursive, dynamically consistent version of the alpha‐maxmin model. In the continuous‐time limit, the resulting dynamic utility function can be represented as a convex mixture between worst and best case, but now at the local, infinitesimal level. We study the properties of the utility function and provide an Arrow–Pratt approximation of the static and dynamic certainty equivalent. We then derive a consumption‐based capital asset pricing formula and study the implications for derivative valuation under indifference pricing.