Date of Completion
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
Field of Study
Doctor of Philosophy
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.
Coster, Berend, "Log-Sobolev Inequality for the Wright-Fisher Diffusion and Optimal Investment with Random Endowments Under Anticipation" (2019). Doctoral Dissertations. 2302.