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  • 1.
    Alm, Jonas
    et al.
    Chalmers.
    Lindskog, Filip
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Foreign-currency interest-rate swaps in asset-liability management for insurers2013In: European Actuarial Journal, ISSN 2190-9733, E-ISSN 2190-9741, Vol. 3, no 1, p. 133-158Article in journal (Refereed)
    Abstract [en]

    We consider an insurer with purely domestic business whose liabilities towards its policy holders have long durations. The relative shortage of domestic government bonds with long maturities makes the insurer’s net asset value sensitive to fluctuations in the zero rates used for liability valuation. Therefore, in order to increase the duration of the insurer’s assets, it is common practice for insurers to take a position as the fixed-rate receiver in an interest-rate swap. We assume that this is not possible in the domestic currency but in a foreign currency supporting a larger market of interest-rate swaps. Monthly data over 16 years are used as the basis for investigating the risks to the future net asset value of the insurer from using foreign-currency interest-rate swaps as a proxy for domestic ones in asset–liability management. We find that although a suitable position in swaps may reduce the standard deviation of the future net asset value it may significantly increase the exposure to tail risk that has a substantial effect on the estimation of the solvency capital requirements.

  • 2. Boman, Jan
    et al.
    Lindskog, Filip
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Support Theorems for the Radon Transform and Cram,r-Wold Theorems2009In: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 22, no 3, p. 683-710Article in journal (Refereed)
    Abstract [en]

    This article presents extensions of the Cram,r-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions imposed are sharp. The extensions build on a number of results and methods concerned with injectivity properties of the Radon transform. Using a few tools from distribution theory and Fourier analysis we show that the presented injectivity results for the Radon transform lead to Cram,r-Wold type results for measures. One purpose of this article is to contribute to making known to probabilists interesting results for the Radon transform that have been developed essentially during the 1980s and 1990s.

  • 3.
    Hult, Henrik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Lindskog, Filip
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Extremal behavior of regularly varying stochastic processes2005In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 115, no 2, p. 249-274Article in journal (Refereed)
    Abstract [en]

    We study a formulation of regular variation for multivariate stochastic processes on the unit interval with sample paths that are almost surely right-continuous with left limits and we provide necessary and sufficient conditions for such stochastic processes to be regularly varying. A version of the Continuous Mapping Theorem is proved that enables the derivation of the tail behavior of rather general mappings of the regularly varying stochastic process. For a wide class of Markov processes with increments satisfying a condition of weak dependence in the tails we obtain simplified sufficient conditions for regular variation. For such processes we show that the possible regular variation limit measures concentrate on step functions with one step, from which we conclude that the extremal behavior of such processes is due to one big jump or an extreme starting point. By combining this result with the Continuous Mapping Theorem, we are able to give explicit results on the tail behavior of various vectors of functionals acting on such processes. Finally, using the Continuous Mapping Theorem we derive the tail behavior of filtered regularly varying Levy processes.

  • 4. Hult, Henrik
    et al.
    Lindskog, Filip
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Extremal behavior of stochastic integrals driven by regularly varying Levy processes2007In: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 35, no 1, p. 309-339Article in journal (Refereed)
    Abstract [en]

    We study the extremal behavior of a stochastic integral driven by a multivariate Levy process that is regularly varying with index alpha > 0. For predictable integrands with a finite (alpha + delta)-moment, for some delta > 0, we show that the extremal behavior of the stochastic integral is due to one big jump of the driving Levy process and we determine its limit measure associated with regular variation on the space of cadlag functions.

  • 5.
    Hult, Henrik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Lindskog, Filip
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Heavy-tailed insurance portfolios: buffer capital and ruin probabilities2006Report (Other academic)
  • 6.
    Hult, Henrik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Lindskog, Filip
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    On Kesten's counterexample to the Cramer-Wold device for regular variation2006In: Bernoulli, ISSN 1350-7265, E-ISSN 1573-9759, Vol. 12, no 1, p. 133-142Article in journal (Refereed)
    Abstract [en]

    In 2002 Basrak, Davis and Mikosch showed that an analogue of the Cramer-Wold device holds for regular variation of random vectors if the index of regular variation is not an integer. This characterization is of importance when studying stationary solutions to stochastic recurrence equations. In this paper we construct counterexamples showing that for integer-valued indices, regular variation of all linear combinations does not imply that the vector is regularly varying. The construction is based on unpublished notes by Harry Kesten.

  • 7. Hult, Henrik
    et al.
    Lindskog, Filip
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    On regular variation for infinitely divisible random vectors and additive processes2006In: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 38, no 1, p. 134-148Article in journal (Refereed)
    Abstract [en]

    We study the tail behavior of regularly varying infinitely divisible random vectors and additive processes, i.e. stochastic processes with independent but not necessarily stationary increments. We show that the distribution of an infinitely divisible random vector is tail equivalent to its Levy measure and we study the asymptotic decay of the probability for an additive process to hit sets far away from the origin. The results are extensions of known univariate results to the multivariate setting; we exemplify some of the difficulties that arise in the multivariate case.

  • 8.
    Hult, Henrik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Lindskog, Filip
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Ruin probabilities under general investments and heavy-tailed claims2011In: Finance and Stochastics, ISSN 0949-2984, E-ISSN 1432-1122, Vol. 15, no 2, p. 243-265Article in journal (Refereed)
    Abstract [en]

    In this paper, the asymptotic decay of finite time ruin probabilities is studied. An insurance company is considered that faces heavy-tailed claims and makes investments in risky assets whose prices evolve according to quite general semimartingales. In this setting, the ruin problem corresponds to determining hitting probabilities for the solution to a randomly perturbed stochastic integral equation. A large deviation result for the hitting probabilities is derived that holds uniformly over a family of semimartingales. This result gives the asymptotic decay of finite time ruin probabilities under sufficiently conservative investment strategies, including ruin-minimizing strategies. In particular, as long as the insurance company invests sufficiently conservatively, the investment strategy has only a moderate impact on the asymptotics of the ruin probability.

  • 9. Hult, Henrik
    et al.
    Lindskog, Filip
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Mikosch, Thomas
    Samorodnitsky, Gennady
    Functional large deviations for multivariate regularly varying random walks2005In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 15, no 4, p. 2651-2680Article in journal (Refereed)
    Abstract [en]

    We extend classical results by A. V. Nagaev [Izv Akad. Nauk UzSSR Ser Fiz.-Mat. Nauk 6 (1969) 17-22, Theory Probab. Appl. 14 (1969) 51-64, 193-208] on large deviations for sums of i.i.d. regularly varying random variables to partial sum processes of i.i.d. regularly varying vectors. The results are stated in terms of a heavy-tailed large deviation principle on the space of cAdlAg functions. We illustrate how these results can be applied to functionals of the partial sum process, including ruin probabilities for multivariate random walks and long strange se-ments. These results make precise the idea of heavy-tailed large deviation heuristics: in an asymptotic sense, only the largest step contributes to the extremal behavior of a multivariate random walk.

  • 10.
    Hult, Henrik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Lindskog, Filip
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Nykvist, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    A simple time-consistent model for the forward density process2013In: International Journal of Theoretical and Applied Finance, ISSN 0219-0249, Vol. 16, no 8, p. 13500489-Article in journal (Refereed)
    Abstract [en]

    In this paper, a simple model for the evolution of the forward density of the future value of an asset is proposed. The model allows for a straightforward initial calibration to option prices and has dynamics that are consistent with empirical findings from option price data. The model is constructed with the aim of being both simple and realistic, and avoid the need for frequent re-calibration. The model prices of n options and a forward contract are expressed as time-varying functions of an (n + 1)-dimensional Brownian motion and it is investigated how the Brownian trajectory can be determined from the trajectories of the price processes. An approach based on particle filtering is presented for determining the location of the driving Brownian motion from option prices observed in discrete time. A simulation study and an empirical study of call options on the S&P 500 index illustrate that the model provides a good fit to option price data.

  • 11.
    Hult, Henrik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Lindskog, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Regular variation for measures on metric spaces2006In: Publications de l'Institut Mathématique (Beograd), ISSN 0350-1302, E-ISSN 1820-7405, Vol. 80, no 94, p. 121-140Article in journal (Refereed)
    Abstract [en]

    The foundations of regular variation for Borel measures on a com- plete separable space S, that is closed under multiplication by nonnegative real numbers, is reviewed. For such measures an appropriate notion of convergence is presented and the basic results such as a Portmanteau theorem, a mapping theorem and a characterization of relative compactness are derived. Regu- lar variation is defined in this general setting and several statements that are equivalent to this definition are presented. This extends the notion of regular variation for Borel measures on the Euclidean space Rd to more general metric spaces. Some examples, including regular variation for Borel measures on Rd, the space of continuous functions C and the Skorohod space D, are provided.

  • 12.
    Lindskog, Filip
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Hult, Henrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Hammarlid, Ola
    Rehn, Carl-Johan
    Risk and portfolio analysis: principles and methods2012Book (Refereed)
  • 13.
    Perninge, Magnus
    et al.
    KTH, School of Electrical Engineering (EES), Electric Power Systems.
    Lindskog, Filip
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Söder, Lennart
    KTH, School of Electrical Engineering (EES), Electric Power Systems.
    Importance Sampling of Injected Powers for Electric Power System Security Analysis2011In: IEEE Transactions on Power Systems, ISSN 0885-8950, E-ISSN 1558-0679, Vol. 27, no 1, p. 3-11Article in journal (Refereed)
    Abstract [en]

    Power system security analysis is often strongly tied with contingency analysis. To improve Monte Carlo simulation, many different contingency selection techniques have been proposed in the literature.

1 - 13 of 13
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