Power Forward Performance in Semimartingale Markets with Stochastic Integrated Factors

• 成果类型: Article
• 署名作者: Bo, Lijun; Capponi, Agostino; Zhou, Chao
• 署名单位: Xidian University; Columbia University; National University of Singapore; National University of Singapore
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.1262
• 发表日期: 2023
• 页码: 288-312
• 关键词: utility maximization; ergodic bsdes; time; portfolio; REPRESENTATION; BOUNDARY; pdes

摘要

We study the forward investment performance process (FIPP) in an incomplete semimartingale market model with closed and convex portfolio constraints, when the investor's risk preferences are of the power form. We provide necessary and sufficient conditions for the existence of such a FIPP. In a semimartingale factor model, we show that the FIPP can be recovered as a triplet of processes that admit an integral representation with respect to semimartingales. Using an integrated stochastic factor model, we relate the factor representation of the triplet of processes to the smooth solution of an ill-posed partial integro-differential Hamilton-Jacobi-Bellman equation. We develop explicit constructions for the class of time-monotone FIPPs, generalizing existing results from Brownian to semimartingale market models.