On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance

Abstract EN

We consider an insurance company whose reserves dynamics follow a diffusion-perturbed risk model.

To reduce its risk, the company chooses to reinsure using proportional or excess-of-loss reinsurance.

Using the Hamilton-Jacobi-Bellman (HJB) approach, we derive a second-order Volterra integrodifferential equation (VIDE) which we transform into a linear Volterra integral equation (VIE) of the second kind.

We then proceed to solve this linear VIE numerically using the block-by-block method for the optimal reinsurance policy that minimizes the ultimate ruin probability for the chosen parameters.

Numerical examples with both light- and heavy-tailed distributions are given.

The results show that proportional reinsurance increases the survival of the company in both light- and heavy-tailed distributions for the Cramér-Lundberg and diffusion-perturbed models.