Dynamic Risk Measures for Processes via Backward Stochastic Differential Equations Associated with Lévy Processes

Abstract

In this paper, we study the dynamic risk measures for processes induced by backward stochastic differential equations driven by Teugel’s martingales associated with Lévy processes (BSDELs). The representation theorem for generators of BSDELs is provided. Furthermore, the time consistency of the coherent and convex dynamic risk measures for processes is characterized by means of the generators of BSDELs. Moreover, the coherency and convexity of dynamic risk measures for processes are characterized by the generators of BSDELs. Finally, we provide two numerical examples to illustrate the proposed dynamic risk measures.

Keywords

• dynamic risk measures for processes
• dynamic convex risk measures
• dynamic coherent risk measures
• backward stochastic differential equations
• lévy processes
• teugel’s martingales