Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/98522
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Title: Non-exponential discounting portfolio management with habit formation
Authors: Liu, J
Lin, L
Yiu, KFC 
Wei, J
Issue Date: Dec-2020
Source: Mathematical control and related fields, Dec. 2020, v. 10, no. 4, p. 761-783
Abstract: This paper studies the portfolio management problem for an individual with a non-exponential discount function and habit formation in finite time. The investor receives a deterministic income, invests in risky assets, buys insurance and consumes continuously. The objective is to maximize the utility of excessive consumption, heritage and terminal wealth. The non-exponential discounting makes the optimal strategy adopted by a naive person time-inconsistent. The equilibrium for a sophisticated person is Nash subgame perfect equilibrium, and the sophisticated person is time-consistent. We calculate the analytical solution for both the naive strategy and equilibrium strategy in the CRRA case and compare the results of the two strategies. By numerical simulation, we find that the sophisticated individual will spend less on consumption and insurance and save more than the naive person. The difference in the strategies of the naive and sophisticated person decreases over time. Furthermore, if an individual of either type is more patient in the future or has a greater tendency toward habit formation, he/she will consume less and buy less insurance, and the degree of inconsistency will also be increased. The sophisticated person's consumption and habit level are initially lower than those of a naive person but are higher in later periods.
Keywords: Non-exponential discounting
Habit formation
Optimal portfolio
Optimal insurance
Extended Hamilton-Jacobi-Bellman equation
Publisher: AIMS Press
Journal: Mathematical control and related fields 
ISSN: 2156-8472
EISSN: 2156-8499
DOI: 10.3934/mcrf.2020019
Rights: © American Institute of Mathematical Sciences
This article has been published in a revised form in Mathematical Control and Related Fields http://dx.doi.org/10.3934/mcrf.2020019. This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works.
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