Characterization of stochastic equilibrium controls by the Malliavin calculus
We derive a characterization of equilibrium controls in continuous-time, time-inconsistent control (TIC) problems using the Malliavin calculus. For this, the classical duality analysis of adjoint BSDEs is replaced with the Malliavin integration by parts. This results into a necessary and sufficient ma...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2022
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| Online Access: | https://hdl.handle.net/10356/156893 |
| _version_ | 1811693438907711488 |
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| author | Nguwi, Jiang Yu Privault, Nicolas |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Nguwi, Jiang Yu Privault, Nicolas |
| author_sort | Nguwi, Jiang Yu |
| collection | NTU |
| description | We derive a characterization of equilibrium controls in continuous-time, time-inconsistent control (TIC) problems using the Malliavin calculus. For this, the classical duality analysis of adjoint BSDEs is replaced with the Malliavin integration by parts. This results into a necessary and sufficient maximum principle which is applied to a linear-quadratic TIC problem, recovering previous results obtained by duality analysis
in the mean-variance case, and extending them to the linear-quadratic setting. We also show that our results apply beyond the linear-quadratic case by treating the generalized Merton problem. |
| first_indexed | 2024-10-01T06:51:41Z |
| format | Journal Article |
| id | ntu-10356/156893 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:51:41Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1568932023-02-28T20:03:44Z Characterization of stochastic equilibrium controls by the Malliavin calculus Nguwi, Jiang Yu Privault, Nicolas School of Physical and Mathematical Sciences Science::Mathematics::Probability theory Stochastic Maximum Principle Spike Perturbation Backward Stochastic Differential Equation Malliavin Calculus We derive a characterization of equilibrium controls in continuous-time, time-inconsistent control (TIC) problems using the Malliavin calculus. For this, the classical duality analysis of adjoint BSDEs is replaced with the Malliavin integration by parts. This results into a necessary and sufficient maximum principle which is applied to a linear-quadratic TIC problem, recovering previous results obtained by duality analysis in the mean-variance case, and extending them to the linear-quadratic setting. We also show that our results apply beyond the linear-quadratic case by treating the generalized Merton problem. Ministry of Education (MOE) Submitted/Accepted version This research is supported by the Ministry of Education, Singapore, under its Tier 1 Grant MOE2018-T1-001-201 RG25/18. 2022-05-04T06:02:04Z 2022-05-04T06:02:04Z 2022 Journal Article Nguwi, J. Y. & Privault, N. (2022). Characterization of stochastic equilibrium controls by the Malliavin calculus. Stochastics and Dynamics, 22(1), 2150054-. https://dx.doi.org/10.1142/S021949372021500543 0219-4937 https://hdl.handle.net/10356/156893 10.1142/S021949372021500543 1 22 2150054 en MOE2018-T1-001-201 RG25/18 Stochastics and Dynamics Electronic version of an article published as Stochastics and Dynamics, 22(1), 2022, 2150054, https://doi.org/10.1142/S0219493721500544 @ copyright World Scientific Publishing Company (https://www.worldscientific.com/doi/abs/10.1142/S0219493721500544). application/pdf |
| spellingShingle | Science::Mathematics::Probability theory Stochastic Maximum Principle Spike Perturbation Backward Stochastic Differential Equation Malliavin Calculus Nguwi, Jiang Yu Privault, Nicolas Characterization of stochastic equilibrium controls by the Malliavin calculus |
| title | Characterization of stochastic equilibrium controls by the Malliavin calculus |
| title_full | Characterization of stochastic equilibrium controls by the Malliavin calculus |
| title_fullStr | Characterization of stochastic equilibrium controls by the Malliavin calculus |
| title_full_unstemmed | Characterization of stochastic equilibrium controls by the Malliavin calculus |
| title_short | Characterization of stochastic equilibrium controls by the Malliavin calculus |
| title_sort | characterization of stochastic equilibrium controls by the malliavin calculus |
| topic | Science::Mathematics::Probability theory Stochastic Maximum Principle Spike Perturbation Backward Stochastic Differential Equation Malliavin Calculus |
| url | https://hdl.handle.net/10356/156893 |
| work_keys_str_mv | AT nguwijiangyu characterizationofstochasticequilibriumcontrolsbythemalliavincalculus AT privaultnicolas characterizationofstochasticequilibriumcontrolsbythemalliavincalculus |