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2015 | 3 | 1 |
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On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

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Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions. Being true multivariate exponential models, they also represent a natural choicewhen modeling default times in credit portfolios. Despite being well-studied on an abstract level, the number of known parametric families is small. Furthermore, for most families only implicit stochastic representations are known. The present paper develops new parametric families of MSMVE distributions in arbitrary dimensions. Furthermore, a convenient stochastic representation is stated for such models, which is helpful with regard to sampling strategies.
Opis fizyczny
  • Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany
  • XAIA Investment GmbH, Sonnenstraße 19, 80331 München, Germany
  • Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany
  • [1] Ballani, F. and Schlather, M. (2011). A construction principle for multivariate extreme value distributions. Biometrika, 98(3):633-645. [Crossref][WoS]
  • [2] Barndorff-Nielsen, O. E.,Maejima, M., and Sato, K.-I. (2006a). Infinite divisibility for stochastic processes and time change. J. Theoret. Probab., 19(2):411-446.
  • [3] Barndorff-Nielsen, O. E.,Maejima, M., and Sato, K.-I. (2006b). Some classes of multivariate infinitely divisible distributions admitting stochastic integral representations. Bernoulli, 12(1):1-33.
  • [4] Barndorff-Nielsen, O. E., Rosinski, J., and Thorbjornsen, S. (2008). General Y-transformations. Alea, 4:131-165.
  • [5] Brigo, D. and Chourdakis, K. (2012). Consistent single- and multi-step sampling of multivariate arrival times: A characterization of self-chaining copulas. Working paper, available at
  • [6] Cherubini, U., Luciano, E., and Vecchiato, W. (2004). Copula Methods in Finance. John Wiley & Sons, Chichester.
  • [7] De Haan, L. (1984). A spectral representation for max-stable processes. Ann. Probab., 12(4):1194-1204. [Crossref]
  • [8] De Haan, L. and Pickands, J. (1986). Stationary min-stable stochastic processes. Probab. Theory Rel. Fields, 72(4):477-492. [Crossref]
  • [9] De Haan, L. and Resnick, S. (1977). Limit theory for multivariate sample extremes. Z. Wahrsch. verw. Gebiete, 40(4):317-337.
  • [10] Durante, F. and Salvadori, G. (2010). On the construction of multivariate extreme value models via copulas. Environmetrics, 21(2):143-161.
  • [11] Es-Sebaiy, K. and Ouknine, Y. (2007). How rich is the class of processes which are infinitely divisible with respect to time? Statist. Probab. Lett., 78(5):537-547. [WoS]
  • [12] Esary, J. D. and Marshall, A. W. (1974). Multivariate distributions with exponential minimums. Ann. Statist., 2:84-98. [Crossref]
  • [13] Fougères, A.-L., Nolan, J. P., and Rootzén, H. (2009). Models for dependent extremes using stable mixtures. Scand. J. Stat., 36(1):42-59.
  • [14] Gudendorf, G. and Segers, J. (2010). Extreme-value copulas. In Jaworski, P., Durante, F., Härdle,W. K., and Rychlik, T., editors, Copula Theory and its Applications, 127-145. Springer, Berlin.
  • [15] Gumbel, E. J. and Goldstein, N. (1964). Analysis of empirical bivariate extremal distributions. J. Amer. Statist. Assoc., 59(307):794-816.
  • [16] Hofmann, D. (2009). Characterization of the D-Norm Corresponding to aMultivariate Extreme Value Distribution. PhD thesis, Universität Würzburg,
  • [17] Hürlimann,W. (2003). Hutchinson-Lai’s conjecture for bivariate extreme value copulas. Statist. Probab. Lett., 61(2):191-198.
  • [18] Jiménez, J. R., Villa-Diharce, E., and Flores, M. (2001). Nonparametric estimation of the dependence function in bivariate extreme value distributions. J. Multivariate Anal., 76(2):159-191. [WoS][Crossref]
  • [19] Joe, H. (1990). Families of min-stable multivariate exponential and multivariate extreme value distributions. Statist. Probab. Lett., 9(1):75-81.
  • [20] Joe, H. (1997). Multivariate Models and Multivariate Dependence Concepts. Chapman & Hall/CRC.
  • [21] Joe, H. (2014). Dependence Modeling with Copulas. Chapman & Hall/CRC.
  • [22] Jurek, Z. J. (1985). Relations between the s-selfdecomposable and selfdecomposable measures. Ann. Probab., 13(2):592- 608. [Crossref]
  • [23] Klenke, A. (2006). Wahrscheinlichkeitstheorie. Springer, Berlin.
  • [24] Kotz, S. and Nadarajah, S. (2000). Extreme Value Distributions: Theory and Applications. Imperial College Press, London.
  • [25] Longin, F. and Solnik, B. (2001). Extreme correlation of international equity markets. J. Finance, 56(2):649-676.
  • [26] Mai, J.-F. (2014). Mutivariate exponential distributions with latent factor structure and related topics. Habilitation Thesis, Technische Universität München,
  • [27] Mai, J.-F. and Scherer, M. (2014). Characterization of extendible distributions with exponential minima via processes that are infinitely divisible with respect to time. Extremes, 17(1):77-95.
  • [28] Mai, J.-F., Scherer, M., and Zagst, R. (2013). CIID frailty models and implied copulas. In Jaworski, P., Durante, F., and Härdle, W. K., editors, Copulae in Mathematical and Quantitative Finance, 201-230. Springer, Berlin.
  • [29] Mansuy, R. (2005). On processes which are infinitely divisible with respect to time. Working paper, 0504408.
  • [30] Molchanov, I. (2008). Convex geometry of max-stable distributions. Extremes, 11(3):235-259.
  • [31] Nelsen, R. B. (2006). An Introduction to Copulas. Springer, New York.
  • [32] Pickands, J. (1989).Multivariate negative exponential and extreme value distributions. In Hüsler, J. and Reiss, R.-D., editors, Extreme Value Theory, 262-274. Springer, New York.
  • [33] Poon, S.-H., Rockinger, M., and Tawn, J. (2004). Extreme value dependence in financial markets: Diagnostics, models, and financial implications. Rev. Financ. Stud., 17(2):581-610. [Crossref]
  • [34] Rajput, B. S. and Rosinski, J. (1989). Spectral representations of infinitely divisible processes. Probab. Theory Rel. Fields, 82(3):451-487. [Crossref]
  • [35] Resnick, S. (1987). Extreme Values, Regular Variation and Point Processes. Springer, New York.
  • [36] Ressel, P. (2013). Homogeneous distributions - and a spectral representation of classical mean values and stable tail dependence functions. J. Multivariate Anal., 117:246-256. [Crossref][WoS]
  • [37] Sato, K.-I. (1999). Lévy processes and infinitely divisible distributions. Cambridge University Press, Cambridge.
  • [38] Sato, K.-I. (2004). Stochastic integrals in additive processes and application to semi-Lévy processes. Osaka J. Math., 41(1):211-236.
  • [39] Schilling, R., Song, R., and Vondracek, Z. (2010). Bernstein Functions. De Gruyter, Berlin.
  • [40] Schönbucher, P. J. and Schubert, D. (2001). Copula-dependent defaults in intensity models. Working paper, http://ssrn. com/abstract=301968.
  • [41] Segers, J. (2012). Max-stable models for multivariate extremes. REVSTAT, 10(1):61-82.
  • [42] Vasicek, O. A. (2002). Loan portfolio value. Risk, 160-162.
  • [43] Williamson, R. (1956). Multiply monotone functions and their Laplace transforms. Duke Math. J., 23(2):189-207. [Crossref]
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