We analyze the asymptotic behavior for a system of fully nonlinear parabolic and elliptic quasi-variational inequalities. These equations are related to robust switching control problems introduced in [E. Bayraktar, A. Cosso, and H. Pham, SIAM J. Control Optim., 54 (2016), pp. 2594-2628]. We prove that, as the time horizon goes to infinity (resp., discount factor goes to zero), the long run average solution to the parabolic system (resp., the limiting discounted solution to the elliptic system) is characterized by a solution of a nonlinear system of ergodic variational inequalities. Our results hold under a dissipativity condition and without any nondegeneracy assumption on the diffusion term. Our approach uses mainly probabilistic arguments and in particular a dual randomized game representation for the solution to the system of variational inequalities.

Ergodicity of robust switching control and nonlinear system of quasi-variational inequalities / E. Bayraktar, A. Cosso, H. Pham. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - 55:3(2017), pp. 1915-1953. [10.1137/15M1023014]

Ergodicity of robust switching control and nonlinear system of quasi-variational inequalities

A. Cosso
Secondo
;
2017

Abstract

We analyze the asymptotic behavior for a system of fully nonlinear parabolic and elliptic quasi-variational inequalities. These equations are related to robust switching control problems introduced in [E. Bayraktar, A. Cosso, and H. Pham, SIAM J. Control Optim., 54 (2016), pp. 2594-2628]. We prove that, as the time horizon goes to infinity (resp., discount factor goes to zero), the long run average solution to the parabolic system (resp., the limiting discounted solution to the elliptic system) is characterized by a solution of a nonlinear system of ergodic variational inequalities. Our results hold under a dissipativity condition and without any nondegeneracy assumption on the diffusion term. Our approach uses mainly probabilistic arguments and in particular a dual randomized game representation for the solution to the system of variational inequalities.
ergodic problem; optimal switching; randomization; stochastic games; system of quasi-variational inequalities
Settore MAT/06 - Probabilita' e Statistica Matematica
Article (author)
File in questo prodotto:
File Dimensione Formato  
Bayraktar, Cosso, Pham - 2017.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 651.06 kB
Formato Adobe PDF
651.06 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/931966
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact