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Time-Consistent Conditional Expectation Under Probability Distortion

We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not subadditive in general, so it is beyond the scope of Peng’s framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic setting is time inconsistency, that is, the usual “tower property” fails. By localizing the probability distortion and restricting to a smaller class of random variables, we introduce a so-called distorted probability and construct a conditional expectation in such a way that it coincides with the original nonlinear expectation at time zero, but has a time-consistent dynamics in the sense that the tower property remains valid. Furthermore, we show that in the continuous time model this conditional expectation corresponds to a parabolic differential equation whose coefficient involves the law of the underlying diffusion. This work is the first step toward a new understanding of nonlinear expectations under probability distortion and will potentially be a helpful tool for solving time-inconsistent stochastic optimization problems.

Ketersediaan

Informasi Detail

Judul Seri

MATHEMATICS OF OPERATIONS RESEARCH; Vol.46 No.3 August 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1149 - 1180

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

TIME INCONSISTENCY
PROBABILITY DISTORTION
NONLINEAR EXPECTATION

Info Detail Spesifik

https://doi.org/10.1287/moor.2020.1101

Pernyataan Tanggungjawab

Jin Ma, Ting-Kam Leonard Wong, Jianfeng Zhang

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