Global Optimization for Automatic Model Points Selection in Life Insurance Portfolios

Ana M Ferreiro,Enrico Ferri,José A García,Carlos Vázquez

doi:10.3390/math9050472

Abstract

Starting from an original portfolio of life insurance policies, in this article we propose a methodology to select model points portfolios that reproduce the original one, preserving its market risk under a certain measure. In order to achieve this goal, we first define an appropriate risk functional that measures the market risk associated to the interest rates evolution. Although other alternative interest rate models could be considered, we have chosen the LIBOR (London Interbank Offered Rate) market model. Once we have selected the proper risk functional, the problem of finding the model points of the replicating portfolio is formulated as a problem of minimizing the distance between the original and the target model points portfolios, under the measure given by the proposed risk functional. In this way, a high-dimensional global optimization problem arises and a suitable hybrid global optimization algorithm is proposed for the efficient solution of this problem. Some examples illustrate the performance of a parallel multi-CPU implementation for the evaluation of the risk functional, as well as the efficiency of the hybrid Basin Hopping optimization algorithm to obtain the model points portfolio.

Highlights

This work deals with the risk management in life insurance companies, which is a key aspect in the insurance industry and in Solventia II regulation
A rigorous framework to measure the risk associated to the replacement of the original portfolio by the model points portfolio is an important task that has not been much addressed in the literature
Y rit tu Asset Liability Management (ALM) is a key process to evaluate the profitability of insurance companies and to manage the assets and liabilities portfolios as well as cash flows with the aim to minimize the risk of loss of the company. In this ALM process, the computation of joint projections of future cashflows associated to both portfolios is mandatory

Summary

Introduction

This work deals with the risk management in life insurance companies, which is a key aspect in the insurance industry and in Solventia II regulation. Asset Liability Management (ALM) is the process of managing the assets and liabilities portfolios as well as cash flows to reduce the firm’s risk of loss It plays a key role in the profitability of insurance companies, see [1,2] and the references therein. From the numerical point of view it mainly consists of computing the joint projections of the future cashflows of assets and liabilities portfolios, which can be done by using Monte Carlo algorithms These kind of portfolios comprise a huge number of policies with several characteristics: maturity, possibility of early cancelation, age of the policy holders, gender, etc. The computation of the projections of the liabilities in original portfolios (containing hundreds of thousands of policies) often becomes a highly demanding computational time objective, making the problem barely tractable even if High Performance Computing (HPC)

Objectives

Methods

Conclusion