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.
Highlights
Let (Ω, F, P) be a probability space and T > 0 be a fixed terminal time
The time-consistency of the coherent and convex dynamic risk measures for processes is characterized by means of the generators of BSDELs
The coherency and convexity of dynamic risk measures for processes are characterized by the generators of BSDELs
Summary
Let (Ω, F , P) be a probability space and T > 0 be a fixed terminal time. Let {Bt , 0 ≤ t < ∞}. BSDELs can be seen as a natural generalization of BSDEs. Nualart and Schoutens [3] provided a martingale representation theorem associated with Lévy processes. We study dynamic risk measures induced by BSDELs. In a financial market, jump dynamics, which might be caused by policy interference, natural accidents, and so on, exist. The time-consistency of the coherent and convex dynamic risk measures for processes is characterized by means of the generators of BSDELs. the coherency and convexity of dynamic risk measures for processes are characterized by the generators of BSDELs. we provide two numerical examples.
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