Linear reflected backward stochastic differential equations arising from vulnerable claims in markets with random horizon

This paper considers the setting governed by (F, ), where F is the "public" flow of information, and is a random time which might not be F-observable. This framework covers credit risk theory and life insurance. In this setting, we assume F being generated by a Brownian motion W and consider a vulnerable claim, whose payment's policy depends essentially on the occurrence of. The hedging problems, in many directions, for this claim led to the question of studying the linear reflected-backward-stochastic differential equations (RBSDE hereafter), equation* split &dYₜ=f (t) d (t) +ZₜdWₓ+dMₜ-dKₜ, Y_=, \\ & Y S 0, , ₀^ (Yₒ--Sₒ-) dKₛ=0 P-a. s. . split equation* This is the objective of this paper. For this RBSDE and without any further assumption on that might neglect any risk intrinsic to its stochasticity, we answer the following: a) What are the sufficient minimal conditions on the data (f, , S, ) that guarantee the existence of the solution to this RBSDE? b) How can we estimate the solution in norm using (f, , S)? c) Is there an F-RBSDE that is intimately related to the current one and how their solutions are related to each other? This latter question has practical and theoretical leitmotivs.