Optimal Consumption, Investment, and Housing Choice: A Dynamic Programming Approach
We investigate a portfolio selection problem involving an agent’s realistic housing service choice, where the agent not only has to choose the size of house to live in, but also has to select between renting and purchasing a house. Adopting a dynamic programming approach, we derive a closed-form sol...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/3/127 |
| _version_ | 1797447082502520832 |
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| author | Qi Li Seryoong Ahn |
| author_facet | Qi Li Seryoong Ahn |
| author_sort | Qi Li |
| collection | DOAJ |
| description | We investigate a portfolio selection problem involving an agent’s realistic housing service choice, where the agent not only has to choose the size of house to live in, but also has to select between renting and purchasing a house. Adopting a dynamic programming approach, we derive a closed-form solution to obtain the optimal policies for the consumption, investment, housing service, and purchasing time for a house. We also present various numerical demonstrations showing the impacts of parameters in the financial and housing markets and the agent’s preference, which visually show the economic implications of our model. Our model makes a significant contribution because it is a pioneering model for the optimal time to purchase a house, which has not been investigated in depth in existing mathematical portfolio optimization models. |
| first_indexed | 2024-03-09T13:50:43Z |
| format | Article |
| id | doaj.art-1785a02f2c4448c39bad37b8a8b1e444 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T13:50:43Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-1785a02f2c4448c39bad37b8a8b1e4442023-11-30T20:50:16ZengMDPI AGAxioms2075-16802022-03-0111312710.3390/axioms11030127Optimal Consumption, Investment, and Housing Choice: A Dynamic Programming ApproachQi Li0Seryoong Ahn1Department of Mathematics, Pusan National University, 2 Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan 46241, KoreaDivision of Business Administration, Pukyong National University, 45 Yongso-ro, Nam-gu, Busan 48513, KoreaWe investigate a portfolio selection problem involving an agent’s realistic housing service choice, where the agent not only has to choose the size of house to live in, but also has to select between renting and purchasing a house. Adopting a dynamic programming approach, we derive a closed-form solution to obtain the optimal policies for the consumption, investment, housing service, and purchasing time for a house. We also present various numerical demonstrations showing the impacts of parameters in the financial and housing markets and the agent’s preference, which visually show the economic implications of our model. Our model makes a significant contribution because it is a pioneering model for the optimal time to purchase a house, which has not been investigated in depth in existing mathematical portfolio optimization models.https://www.mdpi.com/2075-1680/11/3/127housing choicehousing serviceportfolio selectionHamilton–Jacobi–Bellman equationdynamic programming |
| spellingShingle | Qi Li Seryoong Ahn Optimal Consumption, Investment, and Housing Choice: A Dynamic Programming Approach Axioms housing choice housing service portfolio selection Hamilton–Jacobi–Bellman equation dynamic programming |
| title | Optimal Consumption, Investment, and Housing Choice: A Dynamic Programming Approach |
| title_full | Optimal Consumption, Investment, and Housing Choice: A Dynamic Programming Approach |
| title_fullStr | Optimal Consumption, Investment, and Housing Choice: A Dynamic Programming Approach |
| title_full_unstemmed | Optimal Consumption, Investment, and Housing Choice: A Dynamic Programming Approach |
| title_short | Optimal Consumption, Investment, and Housing Choice: A Dynamic Programming Approach |
| title_sort | optimal consumption investment and housing choice a dynamic programming approach |
| topic | housing choice housing service portfolio selection Hamilton–Jacobi–Bellman equation dynamic programming |
| url | https://www.mdpi.com/2075-1680/11/3/127 |
| work_keys_str_mv | AT qili optimalconsumptioninvestmentandhousingchoiceadynamicprogrammingapproach AT seryoongahn optimalconsumptioninvestmentandhousingchoiceadynamicprogrammingapproach |