Expected Log-Utility Maximization Under Incomplete Information and with Cox-Process Observations |
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Authors: | Kazufumi Fujimoto Hideo Nagai Wolfgang J. Runggaldier |
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Affiliation: | 1. Corporate Risk Management Division, The Bank of Tokyo-Mitsubishi UFJ, Ltd., Marunouchi 2-7-1, Chiyoda-ku, Tokyo?, 100-8388, Japan 2. Department of Mathematics, Faculty of Engineering Science, Kansai University, 3-3-35 Yamate-cho, Suita, Osaka?, 564-8680, Japan 3. Center for the Study of Finance and Insurance, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka?, 560-8531, Japan 4. Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Trieste 63, 35121?, Padova, Italy
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Abstract: | 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). |
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