Maria de Lourdes Belchior Afonso
@unl.pt
Mathematics - Faculdade de Ciências e Tecnologia
Univeridade Nova de Lisboa
Scopus Publications
Scholar Citations
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Scopus Publications
Nelson Chibeles-Martins and Lourdes B. Afonso
Elsevier
Nelson Chibeles-Martins and Lourdes B. Afonso
Elsevier
Lourdes B. Afonso, Rui M. R. Cardoso, Alfredo D. Egídio dos Reis, and Gracinda R. Guerreiro
Wiley
For a large motor insurance portfolio, on an open environment, we study the impact of experience rating in finite and continuous time ruin probabilities. We consider a model for calculating ruin probabilities applicable to large portfolios with a Markovian Bonus‐Malus System (BMS), based on claim counts, for an automobile portfolio using the classical risk framework model. New challenges are brought when an open portfolio scenario is introduced. When compared with a classical BMS approach ruin probabilities may change significantly. By using a BMS of a Portuguese insurer, we illustrate and discuss the impact of the proposed formulation on the initial surplus required to target a given ruin probability. Under an open portfolio setup, we show that we may have a significant impact on capital requirements when compared with the classical BMS, by having a significant reduction on the initial surplus needed to maintain a fixed level of the ruin probability.
Maria Isabel Gomes, Lourdes B. Afonso, Nelson Chibeles-Martins, and Joana M. Fradinho
Springer International Publishing
A recently European Commission regulation requires insurance companies to determine the maximum value of insured fire risk policies of all buildings that are partly or fully located within circle of a radius of 200 m. In this work, we present the multi-start local search meta-heuristics that has been developed to solve the real case of an insurance company having more than 400 thousand insured buildings in mainland Portugal. A random sample of the data set was used and the solutions of the meta-heuristic were compared with the optimal solution of a MILP model based on the Maximal Covering Location Problem. The results show the proposed approach to be very efficient and effective in solving the problem.
Lourdes B. Afonso, Rui M. R. Cardoso, Alfredo D. Egídio dos Reis, and Gracinda Rita Guerreiro
Cambridge University Press (CUP)
AbstractMotor insurance is a very competitive business where insurers operate with quite large portfolios, often decisions must be taken under short horizons and therefore ruin probabilities should be calculated in finite time. The probability of ruin, in continuous and finite time, is numerically evaluated under the classical Cramér–Lundberg risk process framework for a large motor insurance portfolio, where we allow for a posteriori premium adjustments, according to the claim record of each individual policyholder. Focusing on the classical model for bonus-malus systems, we propose that the probability of ruin can be interpreted as a measure to decide between different bonus-malus scales or even between different bonus-malus rules. In our work, the required initial surplus can also be evaluated. We consider an application of a bonus-malus system for motor insurance to study the impact of experience rating in ruin probabilities. For that, we used a real commercial scale of an insurer operating in the Portuguese market, and we also work on various well-known optimal bonus-malus scales estimated with real data from that insurer. Results involving these scales are discussed.
Lourdes B. Afonso and Pedro Corte Real
Cambridge University Press (CUP)
AbstractThe quantification of operational risk has to deal with various concerns regarding data, much more than other types of risk which banks and insurers are obliged to manage. One of the main questions that worries both researchers and practitioners is the bias in the data on the operational losses amounts recorded. We support the assertions made by several authors and defend that this concern is serious when modeling operational losses data and, typically, is presented in all the databases. We show that it's possible, based on mild assumptions on the internal procedures put in place to manage operational losses, to make parametric inference using loss data statistics, that is, to estimate the parameters for the losses amounts, taking in consideration the bias that, not being considered, generates a two fold error in the estimators for the mean loss amount and the total loss amount, the former being overvalued and the last undervalued. In this paper, we do not consider the existence of a threshold for which, all losses above, are reported and available for analysis and estimation procedures. In this sense, we follow a different approach to the parametric inference. Here, we consider that the probability that a loss is reported and ends up recorded for analysis, increases with the size of the loss, what causes the bias in the database but, at the same time, we do not consider the existence of a threshold, above which, all losses are recorded. Hence, no loss has probability one of being recorded, in what we defend is a realist framework. We deduce the general formulae, present simulations for common theoretical distributions used to model (operational reported) losses amounts, estimate the impact for not considering the bias factor when estimating the value at risk and estimate the true total operational losses the bank incurred.
Lourdes B. Afonso, Rui M.R. Cardoso, and Alfredo D. Egídio dos Reis
Elsevier BV
We consider the compound Poisson dual risk model, dual to the well known classical risk model for insurance applications, where premiums are regarded as costs and claims are viewed as profits. The surplus can be interpreted as a venture capital like the capital of an economic activity involved in research and development. Like most authors, we consider an upper dividend barrier so that we model the gains of the capital and its return to the capital holders.
Lourdes B. Afonso, Alfredo D. Egídio dos Reis, and Howard R. Waters
Cambridge University Press (CUP)
AbstractThe probability of ruin in continuous and finite time is numerically evaluated in a classical risk process where the premium can be updated according to credibility models and therefore change from year to year. A major consideration in the development of this approach is that it should be easily applicable to large portfolios. Our method uses as a first tool the model developed by Afonso et al. (2009), which is quite flexible and allows premiums to change annually. We extend that model by introducing a credibility approach to experience rating.We consider a portfolio of risks which satisfy the assumptions of the Bühlmann (1967, 1969) or Bühlmann and Straub (1970) credibility models. We compute finite time ruin probabilities for different scenarios and compare with those when a fixed premium is considered.
Lourdes B. Afonso, Alfredo D. Egídio dos Reis, and Howard R. Waters
Cambridge University Press (CUP)
AbstractIn this paper we present a method for the numerical evaluation of the ruin probability in continuous and finite time for a classical risk process where the premium can change from year to year. A major consideration in the development of this methodology is that it should be easily applicable to large portfolios. Our method is based on the simulation of the annual aggregate claims and then on the calculation of the ruin probability for a given surplus at the start and at the end of each year. We calculate the within-year ruin probability assuming a translated gamma distribution approximation for aggregate claim amounts.We illustrate our method by studying the case where the premium at the start of each year is a function of the surplus level at that time or at an earlier time.