Asia-Pacific Financial Markets

, Volume 21, Issue 1, pp 35–66 | Cite as

Expected Log-Utility Maximization Under Incomplete Information and with Cox-Process Observations

  • Kazufumi FujimotoEmail author
  • Hideo Nagai
  • Wolfgang J. Runggaldier


We consider the portfolio optimization problem for the criterion of maximization of expected terminal log-utility. The underlying market model is a regime-switching diffusion model where the regime is determined by an unobservable factor process forming a finite state Markov process. The main novelty is due to the fact that prices are observed and the portfolio is rebalanced only at random times corresponding to a Cox process where the intensity is driven by the unobserved Markovian factor process as well. This leads to a more realistic modeling for many practical situations, like in markets with liquidity restrictions; on the other hand it considerably complicates the problem to the point that traditional methodologies cannot be directly applied. The approach presented here is specific to the log-utility. For power utilities a different approach is presented in the companion paper (Fujimoto et al. in Appl Math Optim 67(1):33–72, 2013).


Portfolio optimization Stochastic control Incomplete information Regime-switching models Cox-process observations Random trading times 


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Copyright information

© Springer Japan 2013

Authors and Affiliations

  • Kazufumi Fujimoto
    • 1
    Email author
  • Hideo Nagai
    • 2
    • 3
  • Wolfgang J. Runggaldier
    • 4
  1. 1.Corporate Risk Management DivisionThe Bank of Tokyo-Mitsubishi UFJ, Ltd.Chiyoda-kuJapan
  2. 2.Department of Mathematics, Faculty of Engineering ScienceKansai UniversitySuitaJapan
  3. 3.Center for the Study of Finance and InsuranceOsaka UniversityToyonakaJapan
  4. 4.Dipartimento di Matematica Pura ed ApplicataUniversità di PadovaPadovaItaly

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