Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows |
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| Institution: | 1. School of International Trade and Economics, Central University of Finance and Economics, China;2. School of Economics, University of Adelaide, Australia;1. Department of Actuarial Science and Applied Statistics, Faculty of Business & Information Science, UCSI University, Jalan Menara Gading, 56000 Cheras, Kuala Lumpur, Malaysia;2. Department of Mathematics, B.C. College, Asansol, West Bengal, India;3. School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor DE, Malaysia;1. College of Plant Protection, Key Laboratory of Pesticide Toxicology & Application Technique, Shandong Agricultural University, Tai''an, Shandong 271018, PR China;2. College of Horticultural Science and Engineering, Shandong Agricultural University, Tai''an, Shandong 271018, PR China;1. New Technologies Plate-Form, Public Hospitals of Paris, Raymond Poincaré Teaching Hospital, Garches, France;2. Physical Medicine and Rehabilitation Department, Public Hospitals of Paris, Raymond Poincaré Teaching Hospital, Garches, France;3. Inserm Unit 1179, Team 3: Technologies and Innovative Therapies Applied to Neuromuscular Diseases, University of Versailles St-Quentin-en-Yvelines, Versailles, France;4. Clinical Innovations Center 1429, Public Hospitals of Paris, Raymond Poincaré Teaching Hospital, Garches, France;5. Physiology–Functional Testing Ward, Public Hospitals of Paris, Raymond Poincaré Teaching Hospital, Garches, France;6. University François Rabelais of Tours, Tours, France;1. Finance Discipline Group, UTS Business School, University of Technology Sydney, Broadway, NSW 2007, Australia;2. Quantitative Finance Research Centre, University of Technology, Sydney, Broadway, NSW 2007, Australia;3. Centre for Applied Macroeconomic Analysis, Australian National University, Canberra, ACT 0200, Australia |
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| Abstract: | In this paper, we propose a multi-period portfolio optimization model with stochastic cash flows. Under the mean–variance preference, we derive the pre-commitment and time-consistent investment strategies by applying the embedding scheme and backward induction approach, respectively. We show that the time-consistent strategy is identical to the optimal open-loop strategy. Also, under the exponential utility preference, we develop the optimal strategy for multi-period investment, which is time-consistent. We show that the above two time-consistent strategies are equivalent in some cases. We compare the pre-commitment and time-consistent strategies under different situations with some numerical simulations. The results indicate that the time-consistent strategy is more stable and secure than pre-commitment strategy under the generalized mean–variance criterion. |
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| Keywords: | Portfolio choice Stochastic cash flows Pre-commitment strategy Time-consistent strategy Exponential utility |
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