Power Forward Performance in Semimartingale Markets with Stochastic Integrated Factors

Lijun Bo (), Agostino Capponi () and Chao Zhou ()
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Lijun Bo: School of Mathematics and Statistics, Xidian University, Xi’an 710126, P.R. China
Agostino Capponi: Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Chao Zhou: Department of Mathematics and Risk Management Institute, National University of Singapore, Singapore 119076

Mathematics of Operations Research, 2023, vol. 48, issue 1, 288-312

Abstract: 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.

Keywords: 3E20; 60J20; 37A50; forward performance process; semimartingale market; portfolio constraints; ill-posed HJB equation; time-monotone process (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:48:y:2023:i:1:p:288-312

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