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dc.contributor.authorLy, Selen_US
dc.identifier.citationLy, S. (2020). Stochastic Orderings by Nonlinear Expectations. Doctoral thesis, Nanyang Technological University, Singapore.en_US
dc.description.abstractWe 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.en_US
dc.publisherNanyang Technological Universityen_US
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).en_US
dc.titleStochastic orderings by nonlinear expectationsen_US
dc.typeThesis-Doctor of Philosophyen_US
dc.contributor.supervisorNicolas Privaulten_US
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US
dc.description.degreeDoctor of Philosophyen_US
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