Seminar by Professor Debora Daniela Escobar, Department of Actuarial Mathematics and Statistics, Heriot-Watt University

We formulate the optimal reinsurance problem maximising cumulative dividend payments in discrete-time, where our decision is the ceding loss function for each stage. Reinsurance is applied to the aggregated loss of each stage, and the reinsurance premium is given by a distortion risk measure. Considering also dividends as part of the decision variable, we maximise our objective under (a) the surplus, and (b) adding a solvency constraint that controls the ruin probability. Thirdly, we solve a last problem, (c) under both constraints when dividends are given by a pre-specified dividend rule. Problems (a)-(b) reduce to solving unconstrained static problems. We find multi-layered optimal policies by minimising the expected loss of the insurer for each stage, moreover, (b) offers a dividend rule that caps the surplus. In contrast, the optimal policy for (c) with the barrier dividend rule can be found by solving constrained problems for each stage, where the constraint imposes an upper bound to the retained losses. We obtain multi-layered policies and propose a Linear Programming (LP) to approximate its deductibles. We show results for the Expected value, Value-at-Risk, Average-Value-at-Risk and Glue Value-at-Risk. The deductibles we estimate show a relationship with the distortion, the barrier, and the income of the insurer.

I joined the Department of Actuarial Mathematics and Statistics in Heriot-Watt University in September 2023. Previously, I was an Assistant Professorial Lecturer in the Department of Statistics in the London School of Economics (LSE), where I was the Program Director of the BSc Actuarial Science. I initially joined LSE as a Fellow in the same department following my PhD. I completed my PhD in the Department of Statistics and Operations Research, at the University of Vienna, under the supervision of Prof Georg Ch. Pflug. I have an MSc in Statistical and Computational Data Analytics from the Complutense University of Madrid and the Technical University of Madrid. I hold a BSc in Mathematics from the Complutense University of Madrid.