Axiomatic characteristics for solutions of reflected backward stochastic differential equations. (English) Zbl 1200.60044
Tang, Shanjian (ed.) et al., Control theory and related topics. In memory of Professor Xunjing Li, Fudan, China, June 3–5, 2005. Hackensack, NJ: World Scientific (ISBN 978-981-270-582-2/hbk). 23-43 (2007).
Summary: In this paper, we introduce the notion of an \(\{{\mathcal F}_t,\;0\leq t\leq T\}\)-consistent dynamic operator with a floor in terms of four axioms. We show that an \(\{{\mathcal F}_t,\;0\leq t\leq T\}\)-consistent dynamic operator \(\{{\mathcal E}_{s,t},\;0\leq s\leq t\leq T\}\) with a continuous upper-bounded floor \(\{S_t,\;0\leq t\leq T\}\), is necessarily represented by the solutions of a backward stochastic differential equation reflected upwards on the floor \(\{S_t,\;0\leq t\leq T\}\), if it is \({\mathcal E}^\mu\)-super-dominated for some \(n > 0\) and if it has the non-increasing and floor-above-invariant property of forward translation.
For the entire collection see [Zbl 1130.93008].
For the entire collection see [Zbl 1130.93008].
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 60A05 | Axioms; other general questions in probability |
| 49N90 | Applications of optimal control and differential games |
| 91B30 | Risk theory, insurance (MSC2010) |
| 91B24 | Microeconomic theory (price theory and economic markets) |
