Abstract:  It has been understood that the“local”existence of the Markowitz’optimal portfolio or the solution to the local-risk minimization problem is guaranteed by some specific mathematical structure on the underlying assets price processes known as “Structure Conditions”. In this paper, we consider a semi-martingale market model, and an arbitrary random time. This random time may model the default time of a firm, the death time of an insured, or any the occurrence time of an event that might impact the market model somehow. By adding additional uncertainty to the market model, via this random time, the structure conditions may fail and hence the Markowitz’s optimal portfolio and other quadratic-optimal portfolios might fail to exist. Our aim is to investigate the impact of this random time on the structure conditions from different perspectives. Our analysis allows us to conclude that under some mild assumptions on the market model and the random time, the structure conditions will remain valid on the one hand. Furthermore, we provide two examples illustrating the importance of these assumptions. On the other hand, we describe the random time models for which the structure conditions are preserved for any market model. These results are elaborated separately for the two contexts of stopping with the random time and incorporating totally a specific class of random times respectively. This talk is based on joint work with Tahir Choulli.

Bio: 邓军，博士，对外经济贸易大学金融学院金融工程系副教授。2014 年毕业于加拿大阿尔伯塔大学 (University of Alberta)，获得数理金融(Mathematical Finance)博士学位。研究领域涉及衍生品定价、风险管理、信息经济学等。研究论文发表在Finance and Stochastics，Stochastic Processes and their Applications, Stochastics和国际金融研究等期刊。