We study a two-player zero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The Hamilton-Jacobi-Bellman-Isaacs (HJBI) partial differential equation (PDE) of the game turns out to be a double-obstacle quasi-variational inequality; therefore the two obstacles are implicitly given. We prove that the upper and lower value functions coincide; indeed we show, by means of the dynamic programming principle for the stochastic differential game, that they are the unique viscosity solution to the HJBI equation, therefore proving that the game admits a value.
Stochastic differential games involving impulse controls and double-obstacle quasi-variational inequalities / A. Cosso. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - 51:3(2013 Jan), pp. 2102-2131. [10.1137/120880094]
Stochastic differential games involving impulse controls and double-obstacle quasi-variational inequalities
A. Cosso
2013
Abstract
We study a two-player zero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The Hamilton-Jacobi-Bellman-Isaacs (HJBI) partial differential equation (PDE) of the game turns out to be a double-obstacle quasi-variational inequality; therefore the two obstacles are implicitly given. We prove that the upper and lower value functions coincide; indeed we show, by means of the dynamic programming principle for the stochastic differential game, that they are the unique viscosity solution to the HJBI equation, therefore proving that the game admits a value.File | Dimensione | Formato | |
---|---|---|---|
1206.1219.pdf
accesso riservato
Tipologia:
Pre-print (manoscritto inviato all'editore)
Dimensione
325.28 kB
Formato
Adobe PDF
|
325.28 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
2013+-+Cosso.pdf
accesso riservato
Tipologia:
Publisher's version/PDF
Dimensione
304.37 kB
Formato
Adobe PDF
|
304.37 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.