Gracinda R. Guerreiro

Bio: Gracinda R. Guerreiro is an academic researcher from Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa. The author has contributed to research in topics: Markov chain & Population. The author has an hindex of 6, co-authored 19 publications receiving 102 citations. Previous affiliations of Gracinda R. Guerreiro include University of Lisbon & Universidade Nova de Lisboa.

An alternative approach to bonus malus

Abstract: Under the assumptions of an open portfolio, i.e., considering that a policyholder can transfer his policy to another insurance company and the continuous arrival of new policyholders into a portfolio which can be placed into any of the bonus classes and not only in the "starting class", we developed a model (Stochastic Vortices Model) to estimate the Long Run Distribution for a Bonus Malus System. These hypothesis render the model quite representative of the reality. With the obtained Long Run Distribution, a few optimal bonus scales were calculated, such as Norberg’s (1979), Borgan, Hoem’s and Norberg’s (1981), Gilde and Sundt’s (1989) and Andrade e Silva’s (1991). To compare our results, since this was the rst application of the model, we used the Classic Model for Bonus Malus and the Open Model developed by Centeno and Andrade e Silva (2001). The results of the Stochastic Vortices and the Open Model are highly similar and quite different from those of the Classic Model. Besides this the distribution of policyholders in the various bonus classes was derived assuming that the entrances followed adequate stochastic models.

Stochastic vortices in periodically reclassified populations

Abstract: Our paper considers open populations with arrivals and departures whose elements are subject to periodic reclassications. These populations will be divided into a nite number of sub-populations. Assuming that: a) entries, reclassications and departures occur at the beginning of the time units; b) elements are reallocated at equally spaced times; c) numbers of new elements entering at the beginning of the time units are realizations of independent Poisson distributed random variables; we use Markov chains to obtain limit results for the relative sizes of the sub-populations corresponding to the states of the chain. Namely we will obtain conditions for stability of the relative sizes for transient and recurrent states as well as for all states. The existence of such stability corresponds to the existence of a stochastic structure based either on the transient or on the recurrent states or even on all states. We call these structures stochastic vortices because the structure is maintained despite entrances, departures and reallocations.

Statistical approach for open bonus malus

Abstract: In this paper, following an open portfolio approach, we show how to estimate a Bonus-malus system evolution. Considering a model for the number of new annual policies, we obtain ML estimators, asymptotic distributions and confidence regions for the expected number of new policies entering the portfolio in each year, as well as for the expected number and proportion of insureds in each bonus class, by year of enrollment. Confidence regions for the distribution of policyholders result in confidence regions for optimal bonus scales. Our treatment is illustrated by an example with numerical results.

On the Evolution and Asymptotic Analysis of Open Markov Populations: Application to Consumption Credit

Abstract: In this paper, we study, by means of randomized sampling, the long-run stability of some open Markov population fed with time-dependent Poisson inputs. We show that state probabilities within transient states converge—even when the overall expected population dimension increases without bound—under general conditions on the transition matrix and input intensities.Following the convergence results, we obtain ML estimators for a particular sequence of input intensities, where the sequence of new arrivals is modeled by a sigmoidal function. These estimators allow for the forecast, by confidence intervals, of the evolution of the relative population structure in the transient states.Applying these results to the study of a consumption credit portfolio, we estimate the implicit default rate.

Measuring the impact of a bonus-malus system in finite and continuous time ruin probabilities for large portfolios in motor insurance

Abstract: Motor 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 Cramer–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.

Long-Term Services and Supports for Older Adults: A Review of Home and Community-Based Services Versus Institutional Care

Abstract: Despite a shift from institutional services toward more home and community-based services (HCBS) for older adults who need long-term services and supports (LTSS), the effects of HCBS have yet to be adequately synthesized in the literature.

Stochastic vortices in periodically reclassified populations

Abstract: Our paper considers open populations with arrivals and departures whose elements are subject to periodic reclassications. These populations will be divided into a nite number of sub-populations. Assuming that: a) entries, reclassications and departures occur at the beginning of the time units; b) elements are reallocated at equally spaced times; c) numbers of new elements entering at the beginning of the time units are realizations of independent Poisson distributed random variables; we use Markov chains to obtain limit results for the relative sizes of the sub-populations corresponding to the states of the chain. Namely we will obtain conditions for stability of the relative sizes for transient and recurrent states as well as for all states. The existence of such stability corresponds to the existence of a stochastic structure based either on the transient or on the recurrent states or even on all states. We call these structures stochastic vortices because the structure is maintained despite entrances, departures and reallocations.