Generalized Optimized Certainty Equivalent with Applications in the Rank-Dependent Utility Model

SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 255-294, March 2024.
Abstract. The classic optimized certainty equivalent (OCE), proposed by Ben-Tal and Teboulle [Manag. Sci., 11 (1986), pp. 1445–1466], employs the classical expected utility model to evaluate the random risk, in which model each decision maker is characterized by a unique probability measure and only outcome uncertainty is assumed. Due to the lack of information, the distribution ambiguity or Knightian uncertainty prevails in reality. We employ the variational preference of Maccheroni, Marinacci, and Rustichini [Econometrica, 74 (2006), pp. 1447–1498] to address the issue and generalize the concept of OCE. In this paper, we introduce a class of optimized certainty equivalent based on the variational preference, give its dual representation based on [math]-divergence, and study its equivalent characterization of positive homogeneity and coherence. As applications, we investigate the properties of optimized certainty equivalent based on the rank-dependent utility (RDU) model. The dual representation of the RDU-based shortfall risk measure proposed by Mao and Cai [Finance Stoch., 2 (2018), pp. 367–393] is also presented.