Optimal Investment of Merton Model for Multiple Investors with Frictions
We investigate the classical optimal investment problem of the Merton model in a discrete time with market friction due to loss of wealth in trading. We consider the case of a finite number of investors, with the friction for each investor represented by a convex penalty function. This model cover t...
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/13/2873 |
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| author | Souhail Chebbi Senda Ounaies |
| author_facet | Souhail Chebbi Senda Ounaies |
| author_sort | Souhail Chebbi |
| collection | DOAJ |
| description | We investigate the classical optimal investment problem of the Merton model in a discrete time with market friction due to loss of wealth in trading. We consider the case of a finite number of investors, with the friction for each investor represented by a convex penalty function. This model cover the transaction costs and liquidity models studied previously in the literature. We suppose that each investor maximizes their utility function over all controls that keep the value of the portfolio after liquidation non-negative. In the main results of this paper, we prove the existence of an optimal strategy of investment by using a new approach based on the formulation of an equivalent general equilibrium economy model via constructing a truncated economy, and the optimal strategy is obtained using a classical argument of limits. |
| first_indexed | 2024-03-11T01:35:18Z |
| format | Article |
| id | doaj.art-7e943a3e858f4e29bf0fc7e7167a7d47 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T01:35:18Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7e943a3e858f4e29bf0fc7e7167a7d472023-11-18T17:02:34ZengMDPI AGMathematics2227-73902023-06-011113287310.3390/math11132873Optimal Investment of Merton Model for Multiple Investors with FrictionsSouhail Chebbi0Senda Ounaies1Research Chair of Financial and Actuarial Studies, Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaCentre d’économie de la Sorbonne, Université Paris 1, Panthéon Sorbonne, 106–112 Boulevard de l’Hôpital, CEDEX 13, 75647 Paris, FranceWe investigate the classical optimal investment problem of the Merton model in a discrete time with market friction due to loss of wealth in trading. We consider the case of a finite number of investors, with the friction for each investor represented by a convex penalty function. This model cover the transaction costs and liquidity models studied previously in the literature. We suppose that each investor maximizes their utility function over all controls that keep the value of the portfolio after liquidation non-negative. In the main results of this paper, we prove the existence of an optimal strategy of investment by using a new approach based on the formulation of an equivalent general equilibrium economy model via constructing a truncated economy, and the optimal strategy is obtained using a classical argument of limits.https://www.mdpi.com/2227-7390/11/13/2873Merton modelmultiple investorspenalty functionsgeneral equilibriumtruncated economyoptimal strategy |
| spellingShingle | Souhail Chebbi Senda Ounaies Optimal Investment of Merton Model for Multiple Investors with Frictions Mathematics Merton model multiple investors penalty functions general equilibrium truncated economy optimal strategy |
| title | Optimal Investment of Merton Model for Multiple Investors with Frictions |
| title_full | Optimal Investment of Merton Model for Multiple Investors with Frictions |
| title_fullStr | Optimal Investment of Merton Model for Multiple Investors with Frictions |
| title_full_unstemmed | Optimal Investment of Merton Model for Multiple Investors with Frictions |
| title_short | Optimal Investment of Merton Model for Multiple Investors with Frictions |
| title_sort | optimal investment of merton model for multiple investors with frictions |
| topic | Merton model multiple investors penalty functions general equilibrium truncated economy optimal strategy |
| url | https://www.mdpi.com/2227-7390/11/13/2873 |
| work_keys_str_mv | AT souhailchebbi optimalinvestmentofmertonmodelformultipleinvestorswithfrictions AT sendaounaies optimalinvestmentofmertonmodelformultipleinvestorswithfrictions |