Research On Estimation Of Distribution Algorithm For Insurance Portfolio Optimization

With the development of modern society,insurance becomes more and more popular as an important part of investment to avoid risks.How to make a suitable portfolio choice among a variety of insurance policies has become a hot issue.However,since the return of insurance policies varies greatly in different scenarios,insurance portfolio problem is always accompanied by large uncertainty.Estimation of distribution algorithm is a kind of stochastic optimization algorithm based on probability distributions.Due to the compatibility of its inherent stochastic and the uncertainty in the optimization,it has great potential to deal with uncertain optimization problems.Therefore,estimation of distribution algorithm is applied in this paper to look for the optimal solution of insurance portfolio problem.However,the strong dependence on uncertain scenarios in insurance portfolio problem leads to great difficulty and challenge for the research on optimization algorithms,including:(1)Since there are many constraints in insurance portfolio problem and it includes both discrete and continuous variables.It is difficult to effectively find the optimal solution with traditional estimation of distribution algorithm due to the complexity of the model.(2)When considering insurance investment for a group,the dimensions of the problem increase exponentially with the increase of possible portfolio choices,which brings a great challenge to the optimization.(3)Due to the dependence on uncertain scenarios in insurance portfolio problem,the expectation return cannot be estimated accurately through the statistical expectation value of the parameter.However,the computational cost of estimating the expectation return with scenario simulation method is very high.(4)Due to the dependence on uncertain scenarios in insurance portfolio problem,the variance of the return is very large.It is difficult to approximate the variance with traditional surrogate models.Based on the above difficulties and challenges,this paper focuses on how to deal with different kinds of insurance portfolio problem and research on EDA in the following four aspects:(1)To solve the difficulty in dealing with the complex single-insured insurance portfolio model,an adaptive estimation of distribution algorithm is proposed.By using massive historical data in the insurance market,a data-driven insurance portfolio model considering several endowment policies with different premium-payout ratios,risks,returns as well as hospitalization policies with different coverages is constructed.An adaptive estimation of distribution algorithm is proposed in this paper to solve the problem,which adaptively chooses the sampling model for new population based on the optimization results.A novel constraint handling mechanism is proposed to ensure the feasibility of the solution.A mixed variables framework is embedded in the algorithm to handle continuous and discrete variables simultaneously.(2)To solve the problem of dimension increasement in group insurance portfolio,a coevolutionary estimation of distribution algorithm is proposed.First,since the return of each insured can be calculated separately,the group insurance portfolio problem can be decomposed into several single-insured insurance portfolio problems.In this way,the dimension of the sub-problems can be reduced compared with the original problem,and a suitable insurance portfolio plan can be found more accurately for each insured.Second,since the investment amount of each insured is limited by the total investable amount of the entire group,the group insurance portfolio problem is indivisible.Therefore,a particle swarm optimization algorithm is employed to optimize the allocation to each insured.(3)To solve the problem of dependence on uncertain scenarios in group insurance portfolio,a clustering estimation of distribution algorithm with simplified simulation is proposed.During the evolution process,only one scenario is simulated to distinguish the solutions in each generation.The fitness value of the problem is the profit in simulation.By this way,the computational resources required for scenario simulation can be reduced greatly.An evaluation mechanism that makes comparisons in each simulated scenario and evaluates the algorithm by considering the performance of each scenario is applied based on this simplified simulation approach.This evaluation mechanism can make full use of the information on the solution in each simulation.(4)To solve the problem that the variance is difficult to estimate in multi-objective group insurance portfolio,a clustering non-dominated sorting estimation of distribution algorithm based on data-driven heuristic estimation model is proposed.Since only an approximative rank of the variance is needed in the nondominated sorting approach to determine the dominance relationship between two solutions,a problem-heuristic estimation model is constructed based on the historical data to approximate the rank of the variance.The Spearman rank correlation coefficient between the estimation model and the variance indicates that it is effective to apply the proposed estimation model as a substitute for the variance when searching for the Pareto-optimal solutions.