Risk/Return/Retention Efficient Frontier Discovery Through Evolutionary Optimization For Non-Life Insurance Portfolio

Policyholder capability to easily and promptly change their insurance cover, in terms of contract conditions and provider, has substantially increased during last decades due to high market competency levels and favourable regulations. Consequently, policyholder behaviour modelling acquired increasing attention since being able to predict costumer reaction to future market’s fluctuations and company’s decision achieved a pivotal role within most mature insurance markets. Integrating existing modelling platform with policyholder behavioural predictions allows companies to create synthetic responding environments where several market projections and company’s strategies can be simulated and, through sets of defined objective functions, compared. In this way, companies are able to identify optimal strategies by means of a Multi-Objective optimization problem where the ultimate goal is to approximate the entire set of optimal solutions defining the so-called Pareto Efficient Frontier. This paper aims to demonstrate how meta-heuristic search algorithms can be promptly implemented to tackle actuarial optimization problems such as the renewal of non-life policies. An evolutionary inspired search algorithm is proposed and compared to a Uniform Monte Carlo Search. Several numerical experiments show that the proposed evolutionary algorithm substantially and consistently outperforms the Monte Carlo Search providing faster convergence and higher frontier approximations.