Geometric L\'evy Process Models in Mathematical Finance
Prof. Yoshio MiyaharaNagoya City University 下午 1:30–2:30 鴻經館 107 室Abstract:
The geometric L\'evy process (GLP) models play very important roles in the field of mathematical finance. They are incomplete market models. It is well-known that the distributions of the log returns from the market data of the asset prices have the asymmetry and the fat tail. The GLP models have those properties in general. Among them the geometric stable process (GSP) model is probably the most important model. The importance of the stable process was discussed by Fama('63). In this talk we shall overview the GLP option pricing models, and explain the properties of these models. After that we shall see that the [GSP \&MEMM] model has many advantages among the models for incomplete markets. We also discuss several applications of GLP models to other problems in the mathematical finance, for example the analysis of credit risk, optimal portfolio theory, etc.