3 Presentations

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  02:00 PM - 02:30 PM

  On the Ruin Problem : New Directions and Applications

  • Manuel Morales, presenter, Université de Montréal

  Expressions for the expected discounted penalty function now exist for a wide range of models, in particular for a general class of Levy insurance risk processes [Biffis and Morales (2010) and Biffis and Kyprianou (2010)]. Indeed, the EDPF encapsulates relevant information about ruin related quantities that are of potential interest in risk management applications. Yet, in order to realize this potential, these expressions must be computationally tractable and they must be based on a finite-time horizon definition of the EDPF. In this talk we review existing models and results while emphasizing the role of the theory of fluctuations in understanding the ruin problem. We also discuss new directions that can be studied with the ultimate aim of designing new path-dependent risk measures from the body of knowledge gathered over the years in Ruin Theory.

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  02:30 PM - 03:00 PM

  Comonotonic Approximations for Sums of Dependent Log-Skew Normal Random Variables

  • Oriol Roch, presenter, Universitat de Barcelona

  We consider the construction of lower convex order bounds, in the sense of Kaas et al. (Insur. Math. Econ. 2000; 27:151–168), to approximate sums of dependent log-skew normal random variables. The dependence structure of these random variables is based on the class of multivariate closed skew-normal (CSN) distribution that appears in González-Farías et al. (Skew-Elliptical Distributions and their Applications. A Journey Beyond Normality, Genton MG (ed.), Chapter 6. Chapman & Hall/CRC: Boca Raton, FL, 2004; 25–42) and which carries several interesting properties of the normal distribution apart from allowing additional parameters to regulate skewness. The bounds that we present are therefore natural extensions to the results presented in Dhaene et al. (Insurance: Mathematics and Economics 2002; 31(2): 133–161; Insurance: Mathematics and Economics 2002b; 31(1):3–33), where bounds for sums of log-normal random variables have been derived. These lower bound approximations are constructed based on the additional information provided by a conditioning variable which when optimally chosen can provide an accurate approximation. We exploit inherent properties of this family of skew-normal distributions in order to choose the optimal conditioning variable. Results of our simulations provide an indication of the performance of these approximations.

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  03:00 PM - 03:30 PM

  Credit Risk: An Actuarial Approach Based on Risk Measures

  • Jose Garrido, presenter, Concordia University
  • Alejandro Balbás, U. Carlos III of Madrid, Spain
  • Ramin Okhrati, U. of Southampton, UK

  Credit risk models share several common characteristics with actuarial risk theory models. Even if the problems studied are different, their solutions are similar, at least in some respects. Rating agencies, like Moody's or Standard and Poor`s use econometrics models with several variables, some quite subjective, to produce their credit ratings. We propose to revisit the problem with a more classical risk-based approach. Classical arbitrage-free, consistent market assumptions rule out price differences that allow risk-free profits at zero cost. Yet, over- or under- estimation of the underlying risks generate such arbitrage opportunities, as with current credit ratings on European bonds. We introduce an alternate ranking based on risk measures.