Optimal consumption and portfolio selection with quadratic utility and a subsistence consumption constraint |
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Authors: | Jung Lim Koo Se Ryoong Ahn Byung Lim Koo Hyeng Keun Koo |
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Institution: | 1. School of Law, University of Texas at Austin, Austin, Texas USA;2. Housing Finance Research Institute, Korea Housing Finance Corporation, Busan, Republic of Korea;3. Department of Financial Engineering, Ajou University, Suwon, Republic of Korea |
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Abstract: | In this article, we analyze the optimal consumption and investment policy of an agent who has a quadratic felicity function and faces a subsistence consumption constraint. The agent's optimal investment in the risky asset increases linearly for low wealth levels. Risk taking continues to increase at a decreasing rate for wealth levels higher than subsistence wealth until it hits a maximum at a certain wealth level, and declines for wealth levels above this threshold. Further, the agent has a bliss level of consumption, since if an agent consumes more than this level she will suffer utility loss. Eventually her risk taking becomes zero at a wealth level which supports her bliss consumption. |
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Keywords: | Portfolio selection quadratic utility subsistence consumption constraint martingale method |
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