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  • 1.
    Bodnar, Taras
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Lindholm, Mathias
    Stockholm University, Faculty of Science, Department of Mathematics.
    Thorsén, Erik
    Stockholm University, Faculty of Science, Department of Mathematics.
    Tyrcha, Joanna
    Stockholm University, Faculty of Science, Department of Mathematics.
    Quantile-based optimal portfolio selectionManuscript (preprint) (Other academic)
  • 2.
    Britton, Tom
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Deijfen, Maria
    Stockholm University, Faculty of Science, Department of Mathematics.
    Lagerås, Andreas N
    Stockholm University, Faculty of Science, Department of Mathematics.
    Lindholm, Mathias
    Stockholm University, Faculty of Science, Department of Mathematics.
    Epidemics on random graphs with tunable clustering2008In: Journal of Applied Probability, ISSN 0021-9002, Vol. 45, no 3, p. 743-756Article in journal (Refereed)
    Abstract [en]

    In this paper a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large outbreak in the epidemic. We investigate how these quantities vary with the clustering in the graph and find that, as the clustering increases, the epidemic threshold decreases. The network is modeled by a random intersection graph, in which individuals are independently members of a number of groups and two individuals are linked to each other if and only if there is at least one group that they are both members of.

  • 3.
    Britton, Tom
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics. Matematisk statistik.
    Deijfen, Mia
    Stockholm University, Faculty of Science, Department of Mathematics. Matematisk statistik.
    N. Lagerås, Andreas
    Lindholm, Mathias
    Stockholm University, Faculty of Science, Department of Mathematics. Matematisk statistik.
    Epidemics on random graphs with tunable clustering2007Report (Other (popular science, discussion, etc.))
  • 4.
    Britton, Tom
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Lindholm, Mathias
    Stockholm University, Faculty of Science, Department of Mathematics.
    The early stage behaviour of a stochastic SIR epidemic with term-time forcing2008Report (Other academic)
  • 5.
    Britton, Tom
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Lindholm, Mathias
    Uppsala universitet.
    Turova, Tatyana
    Lunds universitet.
    A dynamic network in a dynamic population: asymptotic properties2011In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 48, p. 1163-1178Article in journal (Refereed)
    Abstract [en]

    We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the life of a node it creates edges to other nodes, nodes with high social index at higher rate, and edges disappear randomly in time. For this model, we derive a criterion for when a giant connected component exists after the process has evolved for a long period of time, assuming that the node population grows to infinity. We also obtain an explicit expression for the degree correlation rho (of neighbouring nodes) which shows that rho is always positive irrespective of parameter values in one of the two treated submodels, and may be either positive or negative in the other model, depending on the parameters.

  • 6.
    Engsner, Hampus
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Lindholm, Mathias
    Stockholm University, Faculty of Science, Department of Mathematics.
    Lindskog, Filip
    Stockholm University, Faculty of Science, Department of Mathematics.
    Insurance valuation: A computable multi-period cost-of-capital approach2017In: Insurance, Mathematics & Economics, ISSN 0167-6687, E-ISSN 1873-5959, Vol. 72, p. 250-264Article in journal (Refereed)
    Abstract [en]

    We present an approach to market-consistent multi-period valuation of insurance liability cash flows based on a two-stage valuation procedure. First, a portfolio of traded financial instrument aimed at replicating the liability cash flow is fixed. Then the residual cash flow is managed by repeated one-period replication using only cash funds. The latter part takes capital requirements and costs into account, as well as limited liability and risk averseness of capital providers. The cost-of-capital margin is the value of the residual cash flow. We set up a general framework for the cost-of-capital margin and relate it to dynamic risk measurement. Moreover, we present explicit formulas and properties of the cost-of-capital margin under further assumptions on the model for the liability cash flow and on the conditional risk measures and utility functions. Finally, we highlight computational aspects of the cost-of-capital margin, and related quantities, in terms of an example from life insurance.

  • 7.
    Lagerås, Andreas
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics. AFA Insurance, Sweden.
    Lindholm, Mathias
    Stockholm University, Faculty of Science, Department of Mathematics.
    How to ask sensitive multiple-choice questions2019In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469Article in journal (Refereed)
    Abstract [en]

    Motivated by recent failures of polling to estimate populist party support, we propose and analyze two methods for asking sensitive multiple-choice questions where the respondent retains some privacy and therefore might answer more truthfully. The first method consists of asking for the true choice along with a choice picked at random. The other method presents a list of choices and asks whether the preferred one is on the list or not. Different respondents are shown different lists. The methods are easy to explain, which makes it likely that the respondent understands how her privacy is protected and may thus entice her to participate in the survey and answer truthfully. The methods are also easy to implement and scale up.

  • 8.
    Lagerås, Andreas
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Lindholm, Mathias
    Stockholm University, Faculty of Science, Department of Mathematics.
    Issues with the Smith-Wilson method2016In: Insurance, Mathematics & Economics, ISSN 0167-6687, E-ISSN 1873-5959, Vol. 71, p. 93-102Article in journal (Refereed)
    Abstract [en]

    We analyse various features of the Smith Wilson method used for discounting under the EU regulation Solvency II, with special attention to hedging. In particular, we show that all key rate duration hedges of liabilities beyond the Last Liquid Point will be peculiar. Moreover, we show that there is a connection between the occurrence of negative discount factors and singularities in the convergence criterion used to calibrate the model. The main tool used for analysing hedges is a novel stochastic representation of the Smith Wilson method.

  • 9. Lagerås, Andreas N.
    et al.
    Lindholm, Mathias
    Stockholm University, Faculty of Science, Department of Mathematics.
    A note on the component structure in random intersection graphs with tunable clustering2008In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 15, no 1, p. N10-Article in journal (Refereed)
    Abstract [en]

    We study the component structure in random intersection graphs with tunable clustering, and show that the average degree works as a threshold for a phase transition for the size of the largest component. That is, if the expected degree is less than one, the size of the largest component is a.a.s. of logarithmic order, but if the average degree is greater than one, a.a.s. a single large component of linear order emerges, and the size of the second largest component is at most of logarithmic order.

  • 10.
    Lindholm, Mathias
    Stockholm University, Faculty of Science, Department of Mathematics.
    A note on the connection between some classical mortality laws and proportional frailty2017In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 126, p. 76-82Article in journal (Refereed)
    Abstract [en]

    We provide a simple frailty argument that produces the Gompertz-Makeham mortality law as the population hazard rate under the assumption of proportional frailty given a common exponential hazard rate. Further, based on a slight generalisation of the result for the Gompertz-Makeham law the connection to Perks and Beard's mortality laws is discussed. Moreover, we give conditions for which functional forms of the baseline hazard that will yield proper frailty distributions given we want to retrieve a certain overall population hazard within the proportional frailty framework.

  • 11.
    Lindholm, Mathias
    Stockholm University, Faculty of Science, Department of Mathematics.
    On the time to extinction for a two-type version of Bartlett's epidemic model2008In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 212, no 1, p. 99-108Article in journal (Refereed)
    Abstract [en]

    We are interested in how the addition of type heterogeneities affects the long time behaviour of models for endemic diseases. We do this by analysing a two-type version of a model introduced by Bartlett under the restriction of proportionate mixing. This model is used to describe diseases for which individuals switch states according to susceptible infectious recovered and immune, where the immunity is life-long. We describe an approximation of the distribution of the time to extinction given that the process is started in the quasi-stationary distribution, and we analyse how the variance and the coefficient of variation of the number of infectious individuals depends on the degree of heterogeneity between the two types of individuals. These are then used to derive an approximation of the time to extinction. From this approximation we conclude that if we increase the difference in infectivity between the two types the expected time to extinction decreases, and if we instead increase the difference in susceptibility the effect on the expected time to extinction depends on which part of the parameter space we are in, and we can also obtain non-monotonic behaviour. These results are supported by simulations.

  • 12.
    Lindholm, Mathias
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Britton, Tom
    Stockholm University, Faculty of Science, Department of Mathematics.
    Endemic persistence or disease extinction: the effect of population separation into subcommunities.2007In: Theoretical Population Biology, Vol. 72, no 2, p. 253-263Article in journal (Refereed)
  • 13.
    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.
    Estimation of conditional mean squared error of prediction for claims reserving2019In: Annals of Actuarial Science, ISSN 1748-4995, E-ISSN 1748-5002Article in journal (Refereed)
    Abstract [en]

    This paper studies estimation of the conditional mean squared error of prediction, conditional on what is known at the time of prediction. The particular problem considered is the assessment of actuarial reserving methods given data in the form of run-off triangles (trapezoids), where the use of prediction assessment based on out-of-sample performance is not an option. The prediction assessment principle advocated here can be viewed as a generalisation of Akaike’s final prediction error. A direct application of this simple principle in the setting of a data-generating process given in terms of a sequence of general linear models yields an estimator of the conditional mean squared error of prediction that can be computed explicitly for a wide range of models within this model class. Mack’s distribution-free chain ladder model and the corresponding estimator of the prediction error for the ultimate claim amount are shown to be a special case. It is demonstrated that the prediction assessment principle easily applies to quite different data-generating processes and results in estimators that have been studied in the literature.

  • 14.
    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.

  • 15.
    Lindholm, Mathias
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Wahl, Felix
    Stockholm University, Faculty of Science, Department of Mathematics.
    On the variance parameter estimator in general linear modelsManuscript (preprint) (Other academic)
    Abstract [en]

    In the present note we consider general linear models where the covariates may be both random and non-random, and where the only restrictions on the error terms are that they are independent and have finite fourth moments. For this class of models we analyse the variance parameter estimator. In particular we obtain finite sample size bounds for the variance of the variance parameter estimator which are independent of covariate information regardless of whether the covariates are random or not. For the case with random covariates this immediately yields bounds on the unconditional variance of the variance estimator  a situation which in general is analytically intractable. The situation with random covariates is illustrated in an example where a certain vector autoregressive model which appears naturally within the area of insurance mathematics is analysed. Further, the obtained bounds are sharp in the sense that both the lower and upper bound will converge to the same asymptotic limit when scaled with the sample size. By using the derived bounds it is simple to show convergence in mean square of the variance parameter estimator for both random and non-random covariates. Moreover, the derivation of the bounds for the above general linear model is based on a lemma which applies in greater generality. This is illustrated by applying the used techniques to a class of mixed effects models.

  • 16.
    Wahl, Felix
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Lindholm, Mathias
    Stockholm University, Faculty of Science, Department of Mathematics.
    Verrall, Richard
    The collective reserving model2019In: Insurance, Mathematics & Economics, ISSN 0167-6687, E-ISSN 1873-5959, Vol. 87, p. 34-50Article in journal (Refereed)
    Abstract [en]

    This paper sets out a model for analysing claims development data, which we call the collective reserving model (CRM). The model is defined on the individual claim level and it produces separate IBNR and RBNS reserve estimators at the collective level without using any approximations. The CRM is based on ideas from a paper by Verrall, Nielsen and Jessen (VNJ) from 2010 in which a model is proposed that relies on a claim giving rise to a single payment. This is generalised by the CRM to the case of multiple payments per claim. All predictors of outstanding claims payments for the VNJ model are shown to hold for this new model. Moreover, the quasi-Poisson GLM estimation framework will be applicable as well, but without using an approximation. Furthermore, analytical expressions for the variance of the total outstanding claims payments are given, with a subdivision on IBNR and RBNS claims. To quantify the effect of allowing only one payment per claim, the model is related and compared to the VNJ model, in particular by looking at variance inequalities. The double chain ladder (DCL) method is discussed as an estimation method for this new model and it is shown that both the GLM- and DCL-based estimators are consistent in terms of an exposure measure. Lastly, both of these methods are shown to asymptotically reproduce the regular chain ladder reserve estimator when restricting predictions to the lower right triangle without the tail, motivating the chain ladder technique as a large-exposure approximation of this model. 

1 - 16 of 16
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