Date of Completion


Embargo Period



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



Doctor of Philosophy

Open Access

Open Access


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.