CONTRASTANDO A POPPER (RAZÓN Y SOCIEDAD) (Spanish Edition)

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This effect can be assessed mathematically. The PML is defined in terms of a very extreme quantile. The resulting reinsurance structures will then be very complicated to analyze and to evaluate their mitigation or transfer effects analytically, so it may be necessary to use alternative approaches, such as Monte Carlo simulation methods. This is what we do in this paper in order to measure the effect of a complex reinsurance treaty on the risk profile of an insurance company. We compute the pure risk premium, PML as well as a host of results: impact on the insured portfolio, risk transfer effect of reinsurance programs, proportion of times reinsurance is exhausted, percentage of years it was necessary to use the contractual reinstatements, etc.

Since the estimators of quantiles are known to be biased, we explore the alternative of using an Extreme Value approach to complement the analysis. The need to estimate future claims has led to the development of many loss reserving techniques. There are two important problems that must be dealt with in the process of estimating reserves for outstanding claims: one is to determine an appropriate model for the claims process, and the other is to assess the degree of correlation among claim payments in different calendar and origin years.

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We approach both problems here. On the one hand we use a gamma distribution to model the claims process and, in addition, we allow the claims to be correlated. We follow a Bayesian approach for making inference with vague prior distributions. The methodology is illustrated with a real data set and compared with other standard methods. Consider a random sample X1, X2,. Only the sample size, mean and range are recorded and it is necessary to estimate the unknown population mean and standard deviation.

In this paper the estimation of the mean and standard deviation is made from a Bayesian perspective by using a Markov Chain Monte Carlo MCMC algorithm to simulate samples from the intractable joint posterior distribution of the mean and standard deviation. The proposed methodology is applied to simulated and real data. This paper is concerned with the situation that occurs in claims reserving when there are negative values in the development triangle of incremental claim amounts.

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Typically these negative values will be the result of salvage recoveries, payments from third parties, total or partial cancellation of outstanding claims due to initial overestimation of the loss or to a possible favorable jury decision in favor of the insurer, rejection by the insurer, or just plain errors. Some of the traditional methods of claims reserving, such as the chain-ladder technique, may produce estimates of the reserves even when there are negative values.

Historically the chain-ladder method has been used as a gold standard benchmark because of its generalized use and ease of application.

This paper presents a Bayesian model to consider negative incremental values, based on a three-parameter log-normal distribution. The model presented here allows the actuary to provide point estimates and measures of dispersion, as well as the complete distribution for outstanding claims from which the reserves can be derived. It is concluded that the method has a clear advantage over other existing methods.

The BMOM is particularly useful for obtaining post-data moments and densities for parameters and future observations when the form of the likelihood function is unknown and thus a traditional Bayesian approach cannot be used. Also, even when the form of the likelihood is assumed known, in time series problems it is sometimes difficult to formulate an appropriate prior density.

Here, we show how the BMOM approach can be used in two, nontraditional problems.

The first one is conditional forecasting in regression and time series autoregressive models. Specifically, it is shown that when forecasting disaggregated data say quarterly data and given aggregate constraints say in terms of annual data it is possible to apply a Bayesian approach to derive conditional forecasts in the multiple regression model.

The types of constraints conditioning usually considered are that the sum, or the average, of the forecasts equals a given value. This kind of condition can be applied to forecasting quarterly values whose sum must be equal to a given annual value.