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Adjustment Coefficient for Risk Processes in Some Dependent Contexts

Author

Listed:
  • Hélène Cossette

    (Université Laval)

  • Etienne Marceau

    (Université Laval)

  • Véronique Maume-Deschamps

    (Université de Lyon, Université Lyon 1, ISFA)

Abstract

Following Müller and Pflug (Insur Math Econ 28:381–392, 2001) and Nyrhinen (Adv Appl Probab 30:1008–1026, 1998; J Appl Probab 36:733–746, 1999), we study the adjustment coefficient of ruin theory in a context of temporal dependency. We provide a consistent estimator for this coefficient, and perform some simulations.

Suggested Citation

  • Hélène Cossette & Etienne Marceau & Véronique Maume-Deschamps, 2011. "Adjustment Coefficient for Risk Processes in Some Dependent Contexts," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 695-721, December.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:4:d:10.1007_s11009-010-9182-y
    DOI: 10.1007/s11009-010-9182-y
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    References listed on IDEAS

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    1. Muller, Alfred & Pflug, Georg, 2001. "Asymptotic ruin probabilities for risk processes with dependent increments," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 381-392, June.
    2. Cossette, Helene & Landriault, David & Marceau, Etienne, 2004. "Compound binomial risk model in a markovian environment," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 425-443, October.
    3. Gerber, Hans U., 1982. "Ruin theory in the linear model," Insurance: Mathematics and Economics, Elsevier, vol. 1(3), pages 213-217, July.
    4. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
    5. Cossette, Hélène & Marceau, Etienne & Maume-Deschamps, Véronique, 2010. "Discrete-Time Risk Models Based on Time Series for Count Random Variables," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 123-150, May.
    6. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    7. Christ, Ralf & Steinebach, Josef, 1995. "Estimating the adjustment coefficient in an ARMA(p, q) risk model," Insurance: Mathematics and Economics, Elsevier, vol. 17(2), pages 149-161, October.
    8. Mammitzsch, V., 1986. "A note on the adjustment coefficient in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 5(2), pages 147-149, April.
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