On risk reserve under distribution constraints

The purpose of this work is a study of the following insurance reserve model: ${\displaystyle R\left(t\right)=\eta +{\int }_0^{t}p(s,R\left(s\right))ds+{\int }_0^t\sigma (s,R\left(s\right))d{W}_s-Z\left(t\right)}$, t ∈ [0,T], P(η ≥ c) ≥ 1-ϵ, ϵ ≥ 0. Under viability-type assumptions on a pair (p,σ) the estimation γ with the property: ${\displaystyle \in f_{0\le t\le T}P\{R\left(t\right)\ge c\}\ge \gamma }$ is considered.