Stochastic ordering by g-expectations

Sel Ly; Nicolas Privault

doi:10.3934/puqr.2021004

Article Contents

2021, Volume 6, Issue 1: 61-98. Doi: 10.3934/puqr.2021004

This issue Previous Article Improved Hoeffding inequality for dependent bounded or sub-Gaussian random variables Next Article

Stochastic ordering by g-expectations

Sel Ly and
Nicolas Privault^,

School of Physical and Mathematical Sciences, Division of Mathematical Sciences, Nanyang Technological University, Singapore 637371

Email: lysel001@e.ntu.edu.sg, nprivault@ntu.edu.sg
Email: lysel001@e.ntu.edu.sg, nprivault@ntu.edu.sg

Received: October 30, 2019

Accepted: January 05, 2021

Published: March 2021

This research is supported by the Ministry of Education, Singapore (Grant No. MOE2018-T1-001-201)

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Abstract

We derive sufficient conditions for the convex and monotonic g-stochastic ordering of diffusion processes under nonlinear g-expectations and g-evaluations. Our approach relies on comparison results for forward-backward stochastic differential equations and on several extensions of convexity, monotonicity, and continuous dependence properties for the solutions of associated semilinear parabolic partial differential equations. Applications to contingent claim price comparison under different hedging portfolio constraints are provided.

Keywords:

Stochastic ordering,
g-expectation,
g-evaluation,
g-risk measures,
Forward-backward stochastic differential equations,
Parabolic PDEs,
Propagation of convexity.

Mathematics Subject Classification: 60E15; 35B51; 60H10; 60H30.

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References

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