Probability and mathematical finance. Part I. Long range self-avoiding walks above critical dimension. Part II. Finite horizon optical investment and consumption with transaction cost.

摘要

The subject of this thesis work consists of two parts. Part I is in the area of probability, where I obtained the limiting distribution of long range self-avoiding random walks above critical dimension. Part II is in the area of mathematical finance, where regularity and free boundary results were obtained on the finite horizon optimal investment and consumption with transaction cost.