Dynamic Risk Measures for Processes Via Reflected Backward Stochastic Differential Equations with Time Delayed Generators

In this paper, we study the problem of dynamic convex risk measures via reflected backward stochastic differential equations with time delayed generators (RBSDEs with time delayed generators, in short). Under some assumptions on the generators of the equations, we prove that the RBSDEs with a convex monotone generator can define the time-consistent dynamic convex risk measure for processes, thus the relation between the generator and the dynamic convex risk measure for processes is established. Since the generator of this equation depends on the past value of the solution, it is more convincing to be used to measure the risk in the insurance and financial field when the investment strategy or portfolio needs to use the past value to replicate the liability or achieve the target