Geodesic
Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillators
M. Lauriere1 ; Z. Li2 ; L. Mertz2 ; J. Wylie3 ; S. Zuo2
1 ORFE, Princeton University, Princeton, NJ 08540, USA
2 ECNU-NYU Institute of Mathematical Sciences, NYU Shanghai, Shanghai, China
3 Department of Mathematics, City University of Hong Kong, Hong Kong, China
ESAIM. Proceedings, Tome 65 (2019), pp. 425-444.

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We consider the optimal stopping and optimal control problems related to stochastic variational inequalities modeling elasto-plastic oscillators subject to random forcing. We formally derive the corresponding free boundary value problems and Hamilton-Jacobi-Bellman equations which belong to a class of nonlinear partial of differential equations with nonlocal Dirichlet boundary conditions. Then, we focus on solving numerically these equations by employing a combination of Howard’s algorithm and the numerical approach [A backward Kolmogorov equation approach to compute means, moments and correlations of non-smooth stochastic dynamical systems; Mertz, Stadler, Wylie; 2017] for this type of boundary conditions. Numerical experiments are given.
DOI : 10.1051/proc/201965425

M. Lauriere 1 ; Z. Li 2 ; L. Mertz 2 ; J. Wylie 3 ; S. Zuo 2

1 ORFE, Princeton University, Princeton, NJ 08540, USA
2 ECNU-NYU Institute of Mathematical Sciences, NYU Shanghai, Shanghai, China
3 Department of Mathematics, City University of Hong Kong, Hong Kong, China 
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     author = {M. Lauriere and Z. Li and L. Mertz and J. Wylie and S. Zuo},
     title = {Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillators},
     journal = {ESAIM. Proceedings},
     pages = {425--444},
     publisher = {mathdoc},
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     year = {2019},
     doi = {10.1051/proc/201965425},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201965425/}
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M. Lauriere; Z. Li; L. Mertz; J. Wylie; S. Zuo. Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillators. ESAIM. Proceedings, Tome 65 (2019), pp. 425-444. doi : 10.1051/proc/201965425. http://geodesic.mathdoc.fr/articles/10.1051/proc/201965425/

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