Nonlinear Stochastic Optimal Control and Optimal Stopping using the Fokker-Planck Transformation
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918445583433728 |
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| author | Selim, Akan Ganguly, Siddhartha Pakniyat, Ali Tsiotras, Panagiotis |
| author_facet | Selim, Akan Ganguly, Siddhartha Pakniyat, Ali Tsiotras, Panagiotis |
| contents | In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent diffusion, we rewrite the controlled Fokker-Planck equation as a continuity equation driven by a score-corrected velocity field, yielding a deterministic characteristic dynamics that reproduces the marginal law of the stochastic system. Leveraging Stein-type identities, we show that the associated distributional dynamic programming equation admits the same second-order differential operator as the distributional stochastic Hamilton-Jacobi-Bellman formulation. Building on this representation, we formulate an optimal control problem with state-dependent terminal-time assignment and terminal distributional constraints and derive the first-order necessary conditions using variational analysis. We present the conditions both for a common terminal time and for the general case of state-dependent stopping. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_12153 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonlinear Stochastic Optimal Control and Optimal Stopping using the Fokker-Planck Transformation Selim, Akan Ganguly, Siddhartha Pakniyat, Ali Tsiotras, Panagiotis Optimization and Control In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent diffusion, we rewrite the controlled Fokker-Planck equation as a continuity equation driven by a score-corrected velocity field, yielding a deterministic characteristic dynamics that reproduces the marginal law of the stochastic system. Leveraging Stein-type identities, we show that the associated distributional dynamic programming equation admits the same second-order differential operator as the distributional stochastic Hamilton-Jacobi-Bellman formulation. Building on this representation, we formulate an optimal control problem with state-dependent terminal-time assignment and terminal distributional constraints and derive the first-order necessary conditions using variational analysis. We present the conditions both for a common terminal time and for the general case of state-dependent stopping. |
| title | Nonlinear Stochastic Optimal Control and Optimal Stopping using the Fokker-Planck Transformation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.12153 |