Supermodular comparison inequalities in option pricing and information inequalities

• Main Author: Kizildemir, Bunyamin
• Other Authors: Nicolas Privault
• Format: Theses and Dissertations
• Language: English
• Published: 2017
• Subjects: DRNTU::Science::Mathematics::Probability theory
• Online Access: http://hdl.handle.net/10356/69531
• Institution: Nanyang Technological University

This thesis is devoted to find necessary and sufficient conditions for supermodular ordering of Poisson random vectors, to bound option prices for multidimensional Ornstein-Uhlenbeck process and multidimensional jump-diffusion model, and to derive inequalities for information theory measures. First, we find necessary and sufficient conditions for supermodular ordering of Poisson random vectors of a certain structure and then we derive the same necessary and sufficient conditions for supermodular ordering of Binomial random vectors, and in the limit case we recover supermodular ordering of Poisson random vectors and existing results in the literature for Gaussian random vectors. Second, by using stochastic and supermodular ordering we derive sufficient conditions for bounding option prices for multidimensional Ornstein-Uhlenbeck process and multidimensional jump-diffusion model. Lastly, we calculate the entropy and mutual information of multidimensional Brownian motion and Poisson process by using Ito calculus and then we derive some comparison results.