‘On the minimization of the ruin probability of both cedent and reinsurer’ ‘On randomized solutions for optimization problems’
Alexandra Bugalho de Moura
‘On the minimization of the ruin probability of both cedent and reinsurer’
Abstract: We consider the optimal reinsurance problem considering both the direct insurer and the reinsurer points of view.
The two players have conflicting interests, as they both seek to absorb the highest premium proportion, while assuming the least possible risk.
We consider proportional reinsurance and a game where both parties aim to minimize their ruin probabilities.
A set of integro-differential equations describing their ruin probability behaviour is derived, and some preliminary numerical illustrations provided.
Based on those equations, Pareto equilibrium conditions are obtained.
‘On randomized solutions for optimization problems’
Abstract: Randomized solutions have been introduced to optimization problems, mainly due to the fact that many nonlinear problems become convex when randomized solutions are considered.
Many optimization problems in insurance and finance are not convexified by randomized solutions, but spaces of randomized solutions still have useful properties for the study of such problems.
Further, randomized solutions can, in many cases, be provided with meaningful economic interpretations and can be used as a tool in model construction.