Modelling of extremal events in insurance and finance

Abraham B, Ledolter J (1983) Statistical methods for forecasting. John Wiley, New York

Aebi M, Embrechts P, Mikosch T (1992) A large claim index. Mitteilungen der Schweiz. Vereinigung der Versicherungsmathematiker 2:143?156

Asmussen S, Fløe Henriksen L, Klüppelberg C (1992) Large claims approximations for risk processes in a Markovian environment. Preprint

Bachelier L (1900) ?Theory of speculation?, reprinted in Cootner P (ed), 1964. The random character of stock market prices. MIT Press, Cambridge 17?78

Beirlant J, Teugels JL (1992) Modelling large claims in non-life insurance. Insurance: Mathematics and Economics 11:17?29

Bingham NH, Goldie CM, Teugels JL (1987) Regular variation. Cambridge University Press, Cambridge

Clewlow LJ, Xu X (1992) A review of option pricing with stochastic volatility. FORC. Preprint 92/35

Cline DBH (1986) Convolution tails, product tails and domains of attraction. Prob Th Rel Fields 72:529?557

Davis RA, Resnick SI (1985) Limit theory for moving averages of random variables with regularly varying tail probabilities. Ann Prob 13:179?195

Davis RA, Resnick SI (1986) Limit theory for the sample covariance and correlation function of moving averages. Ann Statist 14:533?558

Embrechts P (1983) A property of the generalized inverse Gaussian distribution with some applications. J Appl Prob 20:537?544

Embrechts P (1993) Modelling of catastrophic events in insurance and finance. Published in ?Operations Research '92 GMÖOR?. Eds Karmann A, Mosler K, Schader M, Uebe G. Physica-Verlag, Hamburg 544?546

Embrechts P, Goldie CM, Veraverbeke N (1979) Subexponentiality and infinite divisibility. Z Wahrscheinlichkeitstheorie verw Gebiete 49:335?347

Embrechts P, Grandell J, Schmidli H (1993) Finite-time Lundberg inequalities in the Cox case. Scand Actuarial J, to appear

Embrechts P, Klüppelberg C (1993) Some aspects of insurance mathematics. Th Prob Appl, to appear

Embrechts P, Omey E (1984) A property of longtailed distributions. J Appl Prob 21:80?87

Embrechts P, Pugh D, Smith RL (1985) Statistical extremes and risks. Department of Mathematics. One day course. Lecture Notes Series, Imperial College

Embrechts P, Veraverbeke N (1982) Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insurance: Mathematics and Economics 1:55?72

Fama EF(1965) The behaviour of stock market prices. Journal of Business 38:34?105

Fama EF, Roll R (1968) Some properties of symmetric stable distributions. JASA 63:817?836

Feller W (1971) An introduction to probability theory and its applications. Volume II, 2nd ed. Wiley, New York

Franks JR, Schwartz ES (1992) The stochastic behaviour of market variance implied in the prices of index options. Economic Journal. Also reprinted in Hodges SD (ed) Options. Recent advances in theory and practice. Volume 2. Manchester University Press

Geluk JL, de Haan L (1987) Regular variation extensions and Tauberian theorems. CWI Tract 40, Amsterdam

Gisler A, Reinhard P (1990) Robust credibility. Paper presented at the XXIIth Astin Colloquium, Montreux

Goovaerts MJ, Kaas R, van Heerwaarden AE, Bauwelinckx T (1990) Effective actuarial methods. North-Holland, Amsterdam

Grandell J (1991) Aspects of risk theory. Springer-Verlag, Berlin

Häusler E, Teugels JL (1985) On asymptotic normality of Hill's estimator for the exponent of regular variation. Ann Statist 13:743?756

Heyman DP, Sobel MJ (1982) Stochastic models in operations research. Volume I: Stochastic processes and operating characteristics. McGraw-Hill, New York

Hill BM (1975) A simple general approach to inference about the tail of a distribution. Ann Statist 3:1163?1174

Hogg RV, Klugman SA (1984) Loss distributions. John Wiley, New York

Hull J, White A (1987) The pricing of options on assets with stochastic volatility. Journal of Finance 42:281?300

Iglehart DL, Stone ML (1983) Regenerative simulation for estimating extreme values. Operations Research 31(6): 1145?1166

Jung J (1982) Association of Swedish Insurance Companies, Statistical Department, Stockholm

Karatzas I, Shreve SES (1988) Brownian motion and stochastic calculus. Springer-Verlag, New York

Karplus WJ (1992) The heavens are falling. The scientific prediction of catastrophes in our time. Plenum Press, New York

Keller B, Klüppelberg C (1991) Statistical estimation of large claim distributions. Mitteilungen der Schweiz. Vereinigung der Versicherungsmathematiker 2/1991:203?216

Klüppelberg C (1989) Subexponential distributions and characterization of related classes. Prob Th Rel Fields 82:259?269

Klüppelberg C, Mikosch T (1992a) Spectral estimates and stable processes. Stoch Proc Appl 37 (1993) to appear

Klüppelberg C, Mikosch T (1992b) Some limit theory for the normalized periodogram ofp-stable moving averages. ETH preprint

Künsch HR (1992) Robust methods for credibility. Astin Bulletin 22(1): 33?49

Leadbetter MR, Lindgren G, Rootzén H (1983) Extremes and related properties of random sequences and processes. Springer-Verlag, New York

Locher R (ed) (1992) Risiko, zwischen Chance und Gefahr. Reto Locher und Partner AG, Basel

Mandelbrot B (1963) The variation of certain speculative prices. Journal of Business 36:394?419

Øksendahl B (1992) Stochastic differential equations. Springer-Verlag, Berlin

Panjer H, Willmot G (1992) Insurance risk models. Society of Actuaries, Schaumburg, IL

Pfeifer D (1989) Einführung in die Extremwertstatistik. Teubner, Stuttgart

Pickands J (1971) The two-dimensional Poisson process and extremal processes. J Appl Prob 8:745?756

Ramlau-Hansen H (1988a) A solvency study in non-life insurance. Part 1: Analysis of fire, windstorm, and glass claims. Scand Actuarial J: 3?34

Ramlau-Hansen H (1988b) A solvency study in non-life insurance. Part 2: Solvency margin requirements. Scand Actuarial J: 35?60

Reiss R-D (1989) Approximate distribution of order statistics (with applications to non-parametric statistics). Springer-Verlag, New York

Resnick SI (1987) Extreme values, regular variation, and point processes. Springer-Verlag, New York

Schmidii H (1992) A general insurance risk model. PhD thesis, ETH Zürich

Schwert GW (1989) Why does stock market volatility change over time. Journal of Finance 44: 1115?1153

Seber GAF (1984) Multivariate observations. John Wiley, New York

Sigma (1991) Naturkatastrophen und Grossschäden 1990: Versicherte Schäden erreichen Rekordsumme von 17 Mrd US$. Schweizerische Rückversicherungsgesellschaft 3/91

Smith RL (1987) Estimating tails of probability distributions. Ann Statist 15:1174?1207

Smith RL (1989) Extreme value analysis. Statistical Science 4:367?393

Stam AJ (1973) Regular variation of the tail of a subordinated probability distribution. Adv Appl Prob 5:308?327

Taylor S (1986) Modelling financial time series. John Wiley, Chichester

Turner AL, Weigel EJK (1992) Daily stock market volatility 1928?1989. Management Science 38:1586?1609

Weissman I (1978) Estimation of parameters and large quantiles based on thek largest observations. J Amer Statist Assoc 73:812?815