Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912058012860416 |
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| author | Aquino, Luca De Gennaro Desmettre, Sascha Havrylenko, Yevhen Steffensen, Mogens |
| author_facet | Aquino, Luca De Gennaro Desmettre, Sascha Havrylenko, Yevhen Steffensen, Mogens |
| contents | In intertemporal settings, the multiattribute utility theory of Kihlstrom and Mirman suggests the application of a concave transform of the lifetime utility index. This construction, while allowing time and risk attitudes to be separated, leads to dynamically inconsistent preferences. We address this issue in a game-theoretic sense by formalizing an equilibrium control theory for continuous-time Markov processes. In these terms, we describe the equilibrium strategy and value function as the solution of an extended Hamilton-Jacobi-Bellman system of partial differential equations. We verify that (the solution of) this system is a sufficient condition for an equilibrium and examine some of its novel features. A consumption-investment problem for an agent with CRRA-CES utility showcases our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16525 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time Aquino, Luca De Gennaro Desmettre, Sascha Havrylenko, Yevhen Steffensen, Mogens Mathematical Finance Optimization and Control In intertemporal settings, the multiattribute utility theory of Kihlstrom and Mirman suggests the application of a concave transform of the lifetime utility index. This construction, while allowing time and risk attitudes to be separated, leads to dynamically inconsistent preferences. We address this issue in a game-theoretic sense by formalizing an equilibrium control theory for continuous-time Markov processes. In these terms, we describe the equilibrium strategy and value function as the solution of an extended Hamilton-Jacobi-Bellman system of partial differential equations. We verify that (the solution of) this system is a sufficient condition for an equilibrium and examine some of its novel features. A consumption-investment problem for an agent with CRRA-CES utility showcases our approach. |
| title | Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time |
| topic | Mathematical Finance Optimization and Control |
| url | https://arxiv.org/abs/2407.16525 |