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  • 1.
    Björkwall, Susanna
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Hössjer, Ola
    Stockholm University, Faculty of Science, Department of Mathematics.
    Esbjörn, Ohlsson
    Stockholm University, Faculty of Science, Department of Mathematics.
    Bootstrapping the separation method in claims reserving.2010In: Astin Bulletin: Actuarial Studies in Non-Life Insurance, ISSN 0515-0361, E-ISSN 1783-1350, Vol. 40, no 2, p. 845-869Article in journal (Refereed)
    Abstract [en]

    The separation method was introduced by Verbeek (1972) in order to forecast numbers of excess claims and it was developed further by Taylor (1977) to be applicable to the average claim cost.The separation method differs from the chain-ladder in that when the chain-ladder only assumes claim proportionality between the development years, the separation method also separates the claim delay distribution from influences affecting the calendar years, e.g. inflation. Since the inflation contributes to the uncertainty in the estimate of the claims reserve it is important to consider its impact in the context of risk management, too.

    In this paper we present a method for assessing the prediction error distribution of the separation method. To this end we introduce a parametric framework within the separation model which enables joint resampling of claim counts and claim amounts. As a result, the variability of Taylor's predicted reserves can be assessed by extending the parametric bootstrap techniques of Björkwall et al. (2009). The performance of the bootstrapped separation method and chain-ladder is compared for a real data set.

  • 2.
    Björkwall, Susanna
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Hössjer, Ola
    Stockholm University, Faculty of Science, Department of Mathematics.
    Ohlsson, Esbjörn
    Stockholm University, Faculty of Science, Department of Mathematics.
    Non-parametric and parametric bootstrap techniques for age-to-age development factor methods in stochastic claims reserving.2009In: Scandinavian Actuarial Journal, ISSN 0346-1238, E-ISSN 1651-2030, no 4, p. 306-331Article in journal (Refereed)
    Abstract [en]

    In the literature, one of the main objects of stochastic claims reserving is to find models underlying the chain-ladder method in order to analyze the variability of the outstanding claims, either analytically or by bootstrapping. In bootstrapping these models are used to find a full predictive distribution of the claims reserve, even though there is a long tradition of actuaries calculating the reserve estimate according to more complex algorithms than the chain-ladder, without explicit reference to an underlying model. In this paper we investigate existing bootstrap techniques and suggest two alternative bootstrap procedures, one non-parametric and one parametric, by which the predictive distribution of the claims reserve can be found for other age-to-age development factor methods than the chain-ladder, using some rather mild model assumptions. For illustration, the procedures are applied to three different development triangles.

  • 3.
    Hössjer, Ola
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Eriksson, Bengt
    Järnmalm, Kajsa
    Ohlsson, Esbjörn
    Stockholm University, Faculty of Science, Department of Mathematics.
    Assessing individual unexplained variation in non-life insurance.2009In: Astin Bulletin: Actuarial Studies in Non-Life Insurance, ISSN 0515-0361, E-ISSN 1783-1350, Vol. 39, no 1, p. 249-273Article in journal (Refereed)
    Abstract [en]

    We consider variation of observed claim frequencies in non-life insurance, modeled by Poisson regression with overdispersion. In order to quantify how much variation between insurance policies that is captured by the rating factors, one may use the coefficient of determination, R2, the estimated proportion of total variation explained by the model. We introduce a novel coefficient of individual determination (CID), which excludes noise variance and is defined as the estimated fraction of total individual variation explained by the model. We argue that CID is a more relevant measure of explained variation than R2 for data with Poisson variation. We also generalize previously used estimates and tests of overdispersion and introduce new coefficients of individual explained and unexplained variance.Application to a Swedish three year motor TPL data set reveals that only 0.5% of the total variation and 11% of the total individual variation is explained by a model with seven rating factors, including interaction between sex and age. Even though the amount of overdispersion is small (4.4% of the noise variance) it is still highly significant. The coefficient of variation of explained and unexplained individual variation is 29% and 81% respectively.

  • 4.
    Ohlsson, Esbjörn
    Stockholm University, Faculty of Science, Department of Mathematics. Länsförsäkringar Alliance, Stockholm, Sweden.
    Unallocated loss adjustment expense reserving2016In: Scandinavian Actuarial Journal, ISSN 0346-1238, E-ISSN 1651-2030, no 2, p. 167-180Article in journal (Refereed)
    Abstract [en]

    In non-life insurance, the provision for outstanding claims (the claims reserve) should include future loss adjustment expenses, i.e. administrative expenses to settle the claims, and therefore we have to estimate the expected Unallocated Loss Adjustment Expenses (ULAE) - expenses that are not attributable to individual claims, such as salaries at the claims handling department. The ULAE reserve has received little attention from European actuaries in the literature, supposedly because of the lack of detailed data for estimation and evaluation. Having good estimation procedures will, however, become even more important with the introduction of the Solvency II regulations, which require unbiased estimation of future cash flows for all expenses. We present a model for ULAE at the individual claim level that includes both fixed and variable costs. This model leads to an estimate of the ULAE reserve at the aggregate (line-of-business) level, as demonstrated in a numerical example from a Swedish non-life insurer.

  • 5.
    Ohlsson, Esbjörn
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics. Matematisk statistik.
    Lauzeningks, Jan
    The one-year non-life insurance risk2008Conference paper (Other (popular science, discussion, etc.))
    Abstract [en]

    With few exceptions, the literature on non-life insurance reserve risk has been devoted to the ultimo risk, the risk in the full run-off of the liabilities. This is in contrast to the short time horizon in models for the total risk of the insurance company, and in particular the one-year risk perspective taken in the Solvency II project, and in the computation of risk margins with the Cost-of-Capital method. This paper aims at clarifying the methodology for the one-year risk; in particular we describe a simulation approach to the one-year reserve risk. We also discuss the one-year premium risk and the premium reserve. Finally, we initiate a discussion on the role of risk margins and discounting for the reserve and premium risk.

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