Equilibrium transport with time-inconsistent costs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911013991874560 |
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| author | Bayraktar, Erhan Han, Bingyan |
| author_facet | Bayraktar, Erhan Han, Bingyan |
| contents | Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences in a discrete-time setting. Motivating examples are nonlinear objectives, state-dependent costs, and regularized optimal transport with general $f$-divergence. Under the bicausal constraint, we introduce the concept of equilibrium transport. Existence is proved in the semi-discrete Markovian case and the continuous non-Markovian case with strict quasiconvexity, while uniqueness also holds in the second case. We apply our framework to study mean-variance dynamic matching, nonlinear or state-dependent objectives with Gaussian data, and mismatches in job markets. Numerical results indicate a positive relationship between mismatches and state dependence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_01498 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Equilibrium transport with time-inconsistent costs Bayraktar, Erhan Han, Bingyan Optimization and Control Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences in a discrete-time setting. Motivating examples are nonlinear objectives, state-dependent costs, and regularized optimal transport with general $f$-divergence. Under the bicausal constraint, we introduce the concept of equilibrium transport. Existence is proved in the semi-discrete Markovian case and the continuous non-Markovian case with strict quasiconvexity, while uniqueness also holds in the second case. We apply our framework to study mean-variance dynamic matching, nonlinear or state-dependent objectives with Gaussian data, and mismatches in job markets. Numerical results indicate a positive relationship between mismatches and state dependence. |
| title | Equilibrium transport with time-inconsistent costs |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2302.01498 |