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Power Forward Performance in Semimartingale Markets with Stochastic Integrated Factors

Author

Listed:
  • 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)

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.

Suggested Citation

  • Lijun Bo & Agostino Capponi & Chao Zhou, 2023. "Power Forward Performance in Semimartingale Markets with Stochastic Integrated Factors," Mathematics of Operations Research, INFORMS, vol. 48(1), pages 288-312, February.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:1:p:288-312
    DOI: 10.1287/moor.2022.1262
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