Effectively Tackling Reinsurance Problems by Using Evolutionary and Swarm Intelligence Algorithms

Abstract

This paper is focused on solving different hard optimization problems that arise in the field of insurance and, more specifically, in reinsurance problems. In this area, the complexity of the models and assumptions considered in the definition of the reinsurance rules and conditions produces hard black-box optimization problems (problems in which the objective function does not have an algebraic expression, but it is the output of a system (usually a computer program)), which must be solved in order to obtain the optimal output of the reinsurance. The application of traditional optimization approaches is not possible in this kind of mathematical problem, so new computational paradigms must be applied to solve these problems. In this paper, we show the performance of two evolutionary and swarm intelligence techniques (evolutionary programming and particle swarm optimization). We provide an analysis in three black-box optimization problems in reinsurance, where the proposed approaches exhibit an excellent behavior, finding the optimal solution within a fraction of the computational cost used by inspection or enumeration methods.

Computing probable maximum loss in catastrophe reinsurance portfolios on multi‐core and many‐core architectures

“…Much of the research into the application of high‐performance computing techniques to simulations in the area of risk, specifically the insurance and reinsurance domain, has been conducted in an industrial setting and not published in the scientific literature for competitive reasons. However, this situation is slowly changing with recent papers on parallel catastrophe modelling , risk treaty optimisation and parallel reinsurance risk analytics .…”

Multi-Objective Stochastic Optimization Programs for a Non-Life Insurance Company under Solvency Constraints

“…In the actuarial context, the study conducted in [24] represents a first attempt to analyze and compare the capabilities of genetic programming and the particle swarm algorithm to find optimal solutions with respect to inspection algorithms for reinsurance problems (see also [25] for a precise definition). They concluded that the evolutionary algorithms are excellent options to find good solutions in short computation times.…”

Optimal stop-loss reinsurance: a dependence analysis

“…In [34] and [37], they find the parameters of the reinsurance contract that maximize the joint survival probability, when the premiums of the insurer and the reinsurer are fixed, for an excess of loss risk model when the number of claims follows a Poisson process. Salcedo-Sanz et al [41] solve also this question using evolutionary and swarm intelligence techniques. In [37] the previous analysis is extended to include an optimal split of the premium income between the insurer and the reinsurer, given fixed retention and limiting levels.…”

“…Van Wouwe et al [47] determine the optimal level of excess-loss reinsurance in the case that the ultimate ruin probability is taken as stability criterion. The insurer's survival probability is also considered in [40] and [29], and more recently in [43], [44], [25], [39], [13] and [41]. Guerra and Centeno [28] obtain an optimal reinsurance policy by maximizing the insurer's expected utility.…”