Backward stochastic differential equations with regime-switching and sublinear expectations

Abstract

This paper introduces a backward stochastic differential equation driven by both Brownian motion and a Markov chain (BSDEBM). Regime-switching is also incorporated through its driver. The existence and uniqueness of the solution of the BSDEBM are proved. A comparison theorem is also derived. Filtration consistent sublinear expectations are defined and characterized as solutions to the BSDEBM. The bid and ask prices are then represented using sublinear expectations.

19 pages

References in corpus (4)

• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty
• Reflected and doubly reflected BSDEs with jumps: a priori estimates and comparison
• Dynamically Consistent Nonlinear Evaluations and Expectations
• Sublinear Expectations and Martingales in discrete time