Author:
Kim Mun-Chol,O Hun,Hwang Ho-Jin
Abstract
AbstractIn this paper we study a class of optimal stopping problems under g-expectation, that is, the cost function is described by the solution of backward stochastic differential equations (BSDEs). Primarily, we assume that the reward process is
$L\exp\bigl(\mu\sqrt{2\log\!(1+L)}\bigr)$
-integrable with
$\mu>\mu_0$
for some critical value
$\mu_0$
. This integrability is weaker than
$L^p$
-integrability for any
$p>1$
, so it covers a comparatively wide class of optimal stopping problems. To reach our goal, we introduce a class of reflected backward stochastic differential equations (RBSDEs) with
$L\exp\bigl(\mu\sqrt{2\log\!(1+L)}\bigr)$
-integrable parameters. We prove the existence, uniqueness, and comparison theorem for these RBSDEs under Lipschitz-type assumptions on the coefficients. This allows us to characterize the value function of our optimal stopping problem as the unique solution of such RBSDEs.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference23 articles.
1. Lp-SOLUTIONS FOR REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
2. Uniqueness of solution to scalar BSDEs with;Buckdahn;Electron. Commun. Prob.,2018
3. Existence of solution to scalar BSDEs with;Hu;Electron. Commun. Prob.,2018
4. Lp solutions of reflected BSDEs under monotonicity condition