Abstract:
The problem of ruin probability minimization in the Cramer–Lundberg risk model under excess reinsurance is studied. Together with traditional maximization of the Lundberg characteristic coefficient $R$ is considered the problem of direct calculation of insurer's ruin probability $\psi_r(x)$ as an initial-capital function $x$ under the prescribed level of net-retention $r$. To solve this problem, we propose the excess variant of the Cramer integral equation which is an equivalent to the Hamilton–Jacobi–Bellman equation. The continuation method is used for solving this equation; by means of it is found the analytical solution to the Markov risk model. We demonstrated on a series of standard examples that with any admissible value of $x$ the ruin probability $\psi_x(r):=\psi_r(x)$ is usually a unimodal function $r$. A comparison of the analytic representation of ruin probability $\psi_r(x)$ with its asymptotic approximation with $x\rightarrow\infty$ was conducted.
PACS:02.30.Yy
Presented by the member of Editorial Board:A. I. Kibzun
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