Goal programming to evaluate the profile of the most profitable insurers: an application to the Spanish insurance industry

• Author: María Rubio‐Misas,Ana Isabel González‐Fernández,Francisco Ruiz
• DOI: http://doi.org/10.1111/itor.12787
• Date: 01 November 2020
• Published date: 01 November 2020

Intl. Trans. in Op. Res. 27 (2020) 2976–3006

DOI: 10.1111/itor.12787

INTERNATIONAL

TRANSACTIONS

IN OPERATIONAL

RESEARCH

Goal programming to evaluate the profile of the most profitable

insurers: an application to the Spanish insurance industry

Ana Isabel Gonz´

alez-Fern´

andeza, Mar´

ıa Rubio-Misasband Francisco Ruizc,∗

aPhD Program in Economics and Business, Universidad de M´

alaga, M´

alaga, Spain

bFinance and Accounting Department, Universidad de M´

alaga, M´

alaga, Spain

cApplied Economics (Mathematics) Department, Universidad de M´

alaga, M´

alaga, Spain

E-mail: aigonzalezf@uma.es [Gonz´

alez-Fern´

andez]; mrubiom@uma.es [Rubio-Misas]; rua@uma.es [Ruiz]

Received 10 September 2019; receivedin revised form 23 January 2020; accepted 22 February 2020

Abstract

This paper applies a multiobjective goal programming (GP) model to define the profile of the most profitable

insurers by focusingon 14 fir m-decision variables and considering different scenarios resulting fromthe exoge-

nous change in interest rate and GDP per capita growth variables. Weconsider a detailed database of Spanish

non-life insurers overthe period 2003–2012 taking into account two dimensions of insurers’ results: underwrit-

ing results and investment results. A prior econometric analysis is used to find out relevant relations among

the variables. Next, a GP model is formulatedon the basis of the relationships obtained. The model is tested in

a robust environment, allowing changes in the coefficients of the objective functions, and for several scenarios

regarding crisis/noncrisis situations and changes in interestrates. Wefind that having the stock organizational

form, being an unaffiliatedsingle company and maintaining low levels of investment risk, leverage, and regula-

tory solvency are recommended for result optimization.Growth and reinsurance utilization are not advisable

for optimizing the results, whereas size should be positively emphasized even more in instability periods and

when interest rates increase. The results also show that the optimal level of the diversification/specialization

strategy depends on economic conditions. More specialization is advisable as negative changes in interest

rates increase. However, we find that the optimal values of the diversification variable are higher for the crisis

scenarios compared to the corresponding noncrisis scenarios, suggesting that diversification creates value in

crisis. Further sensitivity analyses show the soundness of the conclusions obtained.

Keywords:goal programming; non-life insurers; operational research (OR) in insurance; profitability;corporate diversifi-

cation

1. Introduction

The most recent financial crisis has revealed that systemic risk in insurance has grown due to in-

creased noncore activities bringing to light the important role played by the activities related to

∗Corresponding author.

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International Transactionsin Operational Research C

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A.I. Gonz´

alez-Fern´

andez et al. / Intl. Trans. in Op. Res. 27 (2020) 2976–3006 2977

the insurance industry’s intermediation function (see e.g., The Geneva Association, 2010; Cum-

mins and Weiss, 2014).1Insurance companies provide two main types of functions: assurance

(underwriting) and intermediation. The first function implies risk-pooling and risk-bearing ser-

vices as well as real financial services related to insured losses. The second function, in the case

of life insurers, is traditionally accomplished through the sale of asset accumulation products

such as cash value life insurance policies and annuities. For non-life insurers, the intermediation

function mainly results from the collection of premiums in advance of claim payments to mini-

mize contract enforcement costs (see e.g., Cummins and Nini, 2002; Cummins and Rubio-Misas,

2006).

Both functions are sources of results for insurers. However, the role that insurers’ decisions/

characteristics play in obtaining these two sources of results may differ and can be conflicting.

Consequently, when evaluating insurers’ results, both dimensions (underwriting results and invest-

ment results) need to be considered (see e.g., Swiss Re, 2018). In terms of optimization, the fact

that insurers’ results is a wide concept comprising several conflict aspects calls for a multiobjective

programming approach. Many multiobjective methods exist either to generate good approxima-

tions of the Pareto-efficient set (a posteriori methods), to find the Pareto-efficient solution that

best fits certain preferential information given by the decision maker (DM, apriorimethods), or

to interactively guide the DM toward their most preferred solution (interactive methods) (see e.g.,

Steuer, 1986 or Miettinen, 1999). Among these methods, goal programming (GP) is one of the

most commonly used methods (Charnes and Cooper, 1961; Ijiri, 1965; Lee, 1972; Ignizio, 1976;

Romero, 1991). In a GP model, the DM attempts to achieve a set of significant goals or tar-

gets that are as close as possible to predetermined aspiration levels. That is, the DM searches for

reasonable solutions (satisfying) that are as close as possible to these predetermined aspiration

levels. As reported in Caballero et al. (2009), GP has been widely applied in many different fields,

including business, and continues to be used nowadays (see e.g., Garc´

ıa-Mart´

ınez et al., 2019,

or Salas-Molina, 2019). Besides the proven practical utility of GP while dealing with real prob-

lems, there are other reasons for choosing it as the appropriate multicriteria tool for this study.

First, GP allows a very flexible modelization, where constraints can be turned into goals if so

desired. Second, it yields in our case simple linear models that are easy to solve using traditional

solvers. Finally, it allows solving the model using different target values and/or weights if the DMs

wish so.

We study Spanish non-life insurers over the 10-year period 2003–2012 and focus on 14 firm-

decision variables that could affect insurer’s results. The period of analysis is characterized by

including the recent financial crisis and instances where negative changes in interest rate affected

the industry. For this reason, we take into account different scenarios resulted from exogenous

change in interest rate and GDP per capita growth variables. The econometric analysis provides

the basis to characterize the objective functions and constraints of the multiobjective programming

approach. Then GP models allow providing optimal values of the objective functions depend-

ing on macroeconomic conditions as well as identifying the optimal profile of the insurers in

terms of profitability and advisable levels for the firm-decision variables according to the different

1Noncore activities of insurers include trading in derivatives, asset lending, asset management, and providing financial

guarantees (see Cummins and Weiss, 2014).

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2020 The Authors.

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2020 International Federation of OperationalResearch Societies