Date of Completion

8-9-2019

Embargo Period

8-9-2019

Keywords

Anticipation, Mathematical Finance, Financial Value of Weak Information, Portfolio Optimization, Discrete market models, Discrete time mathematical finance, insider trading, incomplete markets, binomial model, random endowments, Log-Sobolev inequality, Wright-Fisher diffusion, Two dimensional Wright-Fisher diffusion

Major Advisor

Fabrice Baudoin

Associate Advisor

Oleksii Mostovyi

Associate Advisor

Ambar Sengupta

Field of Study

Mathematics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

We prove a Log-Sobolev inequality for the one-dimensional Wright-Fisher diffusion by proving a $\Gamma_2$ lower bound for this diffusion. The result is extended to the two-dimensional case. In subsequent chapters an explicit formula is derived for the value of weak information in a discrete time model that works for a wide range of utility functions including the logarithmic and power utility. We assume a market with a finite number of assets and a finite number of possible outcomes. Results are given for complete and incomplete markets with random endowments. Explicit calculations are performed for a binomial model with two assets. Results for the continuous time case are also reviewed and discussed.

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