A complete explicit solution to the log-optimal portfolio problem
成果类型：
Article
署名作者：
Goll, T; Kallsen, J
署名单位：
University of Freiburg
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
2003
页码：
774-799
关键词：
摘要：
D. Kramkov and W. Schachermayer [Ann. Appl. Probab. 9 (1999) 904950] proved the existence of log-optimal portfolios under weak assumptions in a very general setting. For many-but not all-cases, T. Goll and J. Kallsen [Stochastic Process. Appl. 89 (2000) 31-48] obtained the optimal solution explicitly in terms of the semimartingale characteristics of the price process. By extending this result, this paper provides a complete explicit characterization of log-optimal portfolios without constraints. Moreover, the results of Goll and Kallsen are generalized here in two further respects: First, we allow for random convex trading constraints. Second, the remaining consumption time-or more generally the consumption clock-may be random, which corresponds to a life-insurance problem. Finally, we consider neutral derivative pricing in incomplete markets.