Continuous-time dynamic risk measures by backward stochastic Volterra integral equations

Abstract

Continuous-time dynamic convex and coherent risk measures are introduced. To obtain existence of such risk measures, backward stochastic Volterra integral equations (BSVIEs, for short) are studied. For such equations, notion of adapted M-solution is introduced, well-posedness is established, duality principles and comparison theorems are presented. Then a class of dynamic convex and coherent risk measures are identified as a component of the adapted M-solutions to certain BSVIEs.

†Dedicated to Professor M.Z. Nashed.

Keywords:

• Backward stochastic Volterra integral equations
• Dynamic risk measure
• Adapted M-solution

Keywords:

• 2000 Mathematics Subject Classifications:
• 91B30
• 91B70
• 60H20

Acknowledgement

This work is supported in part by the NSF grant DMS-0604309.

Notes

†Dedicated to Professor M.Z. Nashed.