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Title: Stochastic orderings by nonlinear expectations
Authors: Ly, Sel
Keywords: Science::Mathematics
Issue Date: 2020
Publisher: Nanyang Technological University
Source: Ly, S. (2020). Stochastic Orderings by Nonlinear Expectations. Doctoral thesis, Nanyang Technological University, Singapore.
Abstract: We study the theory of stochastic order under the nonlinear expectations framework, including g- and G-expectations, which leads to more general concepts of orderings in comparison with the standard linear expectation setting. In a summary of theoretical contributions, we have derived several sufficient conditions for the g- and G-stochastic orderings of diffusion processes and of G-diffusion processes in the sense of convex, increasing convex and monotonic order types. Analogous comparison results for g- and G-risk measures have been proposed as consequences, in terms of concave g- and G-stochastic orderings. In addition, we have derived comparisons results between linear, sublinear and nonlinear expectations. Our approach relies on comparison lemmas for forward-backward, and for G-forward-backward stochastic differential equations, and on several extensions of monotonicity, convexity and continuous dependence property for the solutions of associated semilinear parabolic partial differential equations and Hamilton-Jacobi-Bellman-type equations. Applications to contingent claim price comparison under different hedging portfolio constraints, and to superhedging price comparison under ambiguous coefficients are also provided.
DOI: 10.32657/10356/145282
Rights: This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Theses

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