Doubly reflected BSDEs driven by RCLL martingales under stochastic Lipschitz coefficient. (English) Zbl 1537.60067
Summary: In this paper, we study a backward stochastic differential equation driven by a Right Continuous with Left Limits (RCLL) martingale with two completely separated RCLL barriers. When the coefficient is stochastically Lipschitz, we demonstrate the existence and uniqueness of a square-integrable adapted solution using the penalization method.
Additionally, we provide a fair price for a game contingent claim between two traders with additional exogenous knowledge of the same stock price in a public financial market driven by an Azéma’s martingale. We also determine a saddle point for the game when the obstacles are left upper semi-continuous along stopping times.
Additionally, we provide a fair price for a game contingent claim between two traders with additional exogenous knowledge of the same stock price in a public financial market driven by an Azéma’s martingale. We also determine a saddle point for the game when the obstacles are left upper semi-continuous along stopping times.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60G44 | Martingales with continuous parameter |
Keywords:
doubly reflected backward stochastic differential equations; RCLL martingales; stochastic Lipschitz coefficient; penalization method; Azéma’s martingale; game contingent claims; initial enlargement of filtrationReferences:
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