Dynamic risk measures for processes via backward stochastic differential equations. (English) Zbl 1411.91291
Summary: We provide some time-consistent dynamic convex (resp. coherent) risk measures for processes via backward stochastic differential equations (BSDEs for short), and establish the one-to-one correspondence between the generators of BSDEs and the associated dynamic convex (resp. coherent) risk measures for processes. Furthermore, we show that the dynamic convex (resp. coherent) risk measures for processes via BSDEs coincide with the classical dynamic convex (resp. coherent) risk measures under the framework of Peng’s \(g\)-expectations.
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
dynamic risk measure for processes; dynamic convex risk measure; dynamic coherent risk measure; backward stochastic differential equation; \(g\)-expectationReferences:
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