DM -Artigos em Revistas Internacionais / Articles in International Journals
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- On combining quota-share and excess of lossPublication . Centeno, M. de LourdesThis paper is devoted to the study of the initial reserve, as a function of the retention limit, needed to assure that the probability of ruin, at the end of a certain period of time, is not higher than an agreed value, for an excess of loss treaty. To assess the probability of ruin, the normal and the normal power approximation are used. It is shown that the initial reserve is not in general an increasing function of the retention, having a minimum under fair assumptions.
- A Structural Lagrangean Relaxation for Two-Duty Period Bus Driver Scheduling ProblemsPublication . Paixão, José Pinto; Pato, e Margarida VazThe two-duty period bus driver scheduling problem is a particular case of the generalized set covering problem, min {cTx : Ax ⩾ b, 0 ⩽ x ⩽h and integer) where, each column of the boolean matrix A consists of at most two strings of consecutive ones. Such a denomination for the problem is due to several real life applications, in particular for bus crew scheduling. In this paper, we present a 'structural' lagrangean relaxation and penalties for improving the bounds on the optimum for the problem. Two other lagrangean relaxation approaches, previously reported in the literature, are considered too. A computational study relative to these relaxations was carried out with both randomly generated test problems and real life cases from Rodoviária Nacional, a large mass transport operator in Portugal. The results reported in the paper evidence a better performance for the lagrangean relation approach wich combined with greedy heuristics, yeld a reasonably good and fast procedure for tackling real life problems .
- A structural Lagrangean relaxation for two-duty period bus driver scheduling problemsPublication . Pinto, José Pinto; Pato, Margarida VazThe two-duty period bus driver scheduling problem is a particular case of the generalized set covering problem, min {cTx : Ax ⩾ b, 0 ⩽ x ⩽h and integer) where, each column of the boolean matrix A consists of at most two strings of consecutive ones. Such a denomination for the problem is due to several real life applications, in particular for bus crew scheduling. In this paper, we present a 'structural' lagrangean relaxation and penalties for improving the bounds on the optimum for the problem. Two other lagrangean relaxation approaches, previously reported in the literature, are considered too. A computational study relative to these relaxations was carried out with both randomly generated test problems and real life cases from Rodoviária Nacional, a large mass transport operator in Portugal. The results reported in the paper evidence a better performance for the lagrangean relation approach wich combined with greedy heuristics, yeld a reasonably good and fast procedure for tackling real life problems
- How long is the surplus below zero?Publication . Reis, Alfredo D. Egídio dosAssuming the classical compound Poisson continuous time surplus process, we consider the process as continuing if ruin occurs. Due to the assumptions presented, the surplus will go to infinity with probability one. If ruin occurs the process will temporarily stay below the zero level. The purpose of this paper is to find some features about how long the surplus will stay below zero. Using a martingale method we find the moment generating function of the duration of negative surplus, which can be multiple, as well as some moments. We also present the distribution of the number of negative surpluses. We further show that the distribution of duration time of a negative surplus is the same as the distribution of the time of ruin, given ruin occurs and initial surplus is zero. Finally, we present two examples, considering exponential and Gamma(2,β) individual claim amount distributions.
- Ruin problems and dual eventsPublication . Dickson, David C. M.; Reis, Alfredo D. Egídio dosDickson (1992) uses dual events to explain results relating to the distribution of the surplus immediately prior to ruin in the classical surplus process. In this paper we show that dual events can be used to explain other results in ruin theory. In particular we prove and explain the relationship between the density of the surplus immediately prior to ruin, and the joint density of the surplus immediately prior to ruin and the severity of ruin
- Symmetric equilibria for a beam with a nonlinear elastic foundationPublication . Grossinho, Maria do Rosário; Ma, T. F.We study the existence of symmetric solutions of a nonlinear fourth order O.D.E. with nonlinear boundary conditions arising in the theory of elastic beams. Variational methods are used, namely, duality, minimization and mountain pass.
- The effect of the retention limit on the risk reservePublication . Centeno, M. de LourdesThis paper is devoted to the study of the initial reserve, as a function of the retention limit, needed to assure that the probability of ruin, at the end of a certain period of time, is not higher than an agreed value, for an excess of loss treaty. To assess the probability of ruin, the normal and the normal power approximation are used. It is shown that the initial reserve is not in general an increasing function of the retention, having a minimum under fair assumptions.
- On the distribution of the duration of negative surplusPublication . Dickson, David C.M.; Reis, Alfredo D. Egídio dosIn the classical risk model we allow the surplus process to continue if the surplus falls below zero. We consider the distributions of the duration of a single period of negative surplus and of the total duration of negative surplus. We derive explicit results where possible and show how to approximate these distributions.
- Some stable algorithms in ruin theory and their applicationPublication . Dickson, David C. M.; Reis, Alfredo D. Egidio dos; Waters, Howard R.In this paper we present a stable recursive algorithm for the calculation of the probability of ultimate ruin in the classical risk model. We also present stable recursive algorithms for the calculation of the joint and marginal distributions of the surplus prior to ruin and the severity of ruin. In addition we present bounds for these distributions
- Model selection and forecasting of long-range dependent processesPublication . Crato, Nuno; Ray, BonnieFractionally integrated autoregressive moving-average (ARFIMA) models have proved useful tools in the analysis of time series with long-range dependence. However, little is known about various practical issues regarding model selection and estimation methods, and the impact of selection and estimation methods on forecasts. By means of a large-scale simulation study, we compare three different estimation procedures and three automatic model-selection criteria on the basis of their impact on forecast accuracy. Our results endorse the use of both the frequency domain Whittle estimation procedure and the time-domain approximate MLE procedure of Haslett and Raftery in conjunction with the AIC and SIC selection criteria, but indicate that considerable care should be exercised when using ARFIMA models. In general, we find that simple ARMA models provide competitive forecasts. Only a large number of observations and a strongly persistent time series seem to justify the use of ARFIMA models for forecasting purposes..