Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Not available / text

This thesis studies the problem of optimal mass transportation with linear constraints -- supermartingale and martingale transport in discrete and continuous time. Appropriate versions of corresponding dual problems are introduced and shown to satisfy fundamental properties: weak duality, absence of a duality gap, and the existence of a dual optimal element. We show how the existence of a dual optimizer implies that primal optimizers can be characterized geometrically through their support -- an infinite dimensional analogue of complementary slackness. In discrete time martingale and supermartingale transport problems, we utilize this result to establish the existence of canonical transport plans, that is joint optimizers for large families of reward functions. To this end, we show that the optimal support coincides for these families. We additionally characterize these transport plans through order-theoretic minimality properties, with respect to second stochastic order and convex order, respectively, in the supermartingale and the martingale case. This characterization further shows that the canonical transport plan is unique.

Thesis (Ph. D.)--University of Chicago, Dept. of Statistics, June 2001. / Includes bibliographical references. Also available on the Internet.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfillment of the requirements for the degree of Doctor of Philosophy, April 2013. / In a series of papers by Wen-Chi Kuo, Coenraad Labuschagne and Bruce Watson results of martingale theory were generalised to the abstract setting of Riesz spaces. This thesis presents a survey of those results proved and aims to expand upon the work of these authors. In particular, independence results will be considered and these will be used to generalise well known results in the theory of Markov processes to Riesz spaces. Mixingales and quasi-martingales will be translated to the Riesz space setting.

In this thesis, we study the strict local martingale property of solutions of various types of stochastic differential equations and the effect of an initial expansion of the filtration on this property. For the models we consider, we either use existing criteria or, in the case where the stochastic differential equation has jumps, develop new criteria that can can detect the presence of the strict local martingale property. We develop deterministic sufficient conditions on the drift and diffusion coefficient of the stochastic process such that an enlargement by initial expansion of the filtration can produce a strict local martingale from a true martingale. We also develop a way of characterizing the martingale property in stochastic volatility models where the local martingale has a general diffusion coefficient.

No description available.

Bibliography: leaves 171-175. / ix, 175 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1994

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 51-53). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 51-53). Also available on the Internet.