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  • 1. Alm, Jonas
    et al.
    Lindskog, Filip
    Stockholm University, Faculty of Science, Department of Mathematics.
    Valuation of Index-Linked Cash Flows in a Heath-Jarrow-Morton Framework2015In: Risks, ISSN 1670-0139, E-ISSN 2227-9091, Vol. 3, no 3, p. 338-364Article in journal (Refereed)
    Abstract [en]

    In this paper, we study the valuation of stochastic cash flows that exhibit dependence on interest rates. We focus on insurance liability cash flows linked to an index, such as a consumer price index or wage index, where changes in the index value can be partially understood in terms of changes in the term structure of interest rates. Insurance liability cash flows that are not explicitly linked to an index may still be valued in our framework by interpreting index returns as so-called claims inflation, i.e., an increase in claims cost per sold insurance contract. We focus primarily on the case when a deep and liquid market for index-linked contracts is absent or when the market price data are unreliable. Firstly, we present an approach for assigning a monetary value to a stochastic cash flow that does not require full knowledge of the joint dynamics of the cash flow and the term structure of interest rates. Secondly, we investigate in detail model selection, estimation and validation in a Heath-Jarrow-Morton framework. Finally, we analyze the effects of model uncertainty on the valuation of the cash flows and how forecasts of cash flows and interest rates translate into model parameters and affect the valuation.

  • 2.
    Bodnar, Taras
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Gupta, Arjun K.
    Vitlinskyi, Valdemar
    Zabolotskyy, Taras
    Statistical Inference for the Beta Coefficient2019In: Risks, ISSN 1670-0139, E-ISSN 2227-9091, Vol. 7, no 2, article id 56Article in journal (Refereed)
    Abstract [en]

    The beta coefficient plays a crucial role in finance as a risk measure of a portfolio in comparison to the benchmark portfolio. In the paper, we investigate statistical properties of the sample estimator for the beta coefficient. Assuming that both the holding portfolio and the benchmark portfolio consist of the same assets whose returns are multivariate normally distributed, we provide the finite sample and the asymptotic distributions of the sample estimator for the beta coefficient. These findings are used to derive a statistical test for the beta coefficient and to construct a confidence interval for the beta coefficient. Moreover, we show that the sample estimator is an unbiased estimator for the beta coefficient. The theoretical results are implemented in an empirical study.

  • 3.
    Lindholm, Mathias
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Lindskog, Filip
    Stockholm University, Faculty of Science, Department of Mathematics.
    Wahl, Felix
    Stockholm University, Faculty of Science, Department of Mathematics.
    Valuation of Non-Life Liabilities from Claims Triangles2017In: Risks, ISSN 1670-0139, E-ISSN 2227-9091, Vol. 53, no 3, article id 39Article in journal (Refereed)
    Abstract [en]

    This paper provides a complete program for the valuation of aggregate non-life insurance liability cash flows based on claims triangle data. The valuation is fully consistent with the principle of valuation by considering the costs associated with a transfer of the liability to a so-called reference undertaking subject to capital requirements throughout the runoff of the liability cash flow. The valuation program includes complete details on parameter estimation, bias correction and conservative estimation of the value of the liability under partial information. The latter is based on a new approach to the estimation of mean squared error of claims reserve prediction.

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