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Articles

Ruin under stochastic dependence between premium and claim arrivals

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Pages 505-513 | Received 18 Mar 2017, Accepted 04 Sep 2017, Published online: 24 Oct 2017

References

  • Albrecher, H. & Boxma, O. J. (2004). A ruin model with dependence between claim sizes and claim intervals. Insurance: Mathematics and Economics 35, 245–254.
  • Albrecher, H., Boxma, O. J. & Ivanovs, J. (2014). On simple ruin expressions in dependent Sparre Andersen risk models. Journal of Applied Probability 51, 293–296.
  • Albrecher, H., Constantinescu, C. & Loisel, S. (2011). Explicit ruin formulas for models with dependence among risks. Insurance: Mathematics and Economics 48, 265–270.
  • Albrecher, H. & Gerber, H. U. (2010). A direct approach to the discounted penalty function. North American Actuarial Journal 14, 420–434.
  • Albrecher, H. & Teugels, J. L. (2006). Exponential behavior in the presence of dependence in risk theory. Journal of Applied Probability 43, 257–273.
  • Asmussen, S. (2000). Ruin probabilities. Advanced Series in Dynamical Systems. Singapore: World Scientific.
  • Asmussen, S. & Albrecher, H. (2010). Ruin probabilities. Advanced Series on Statistical Science & Applied Probability. Singapore: World Scientific.
  • Bao, Z. (2006). The expected discounted penalty at ruin in the risk process with random income. Applied Mathematics and Computation 179, 559–566.
  • Boikov, A. V. (2003). The Cramér-Lundberg model with stochastic premium process. Theory of Probability & Its Applications 47, 489–493.
  • Bondarev, B. V. & Boldyreva, V. O. (2014). Deriving the equation for the non-ruin probability of the insurance company in (B, S)-market. Stochastic claims and stochastic premiums, Cybernetics and Systems Analysis 50, 750–758.
  • Boudreault, M., Cossette, H., Landriault, D. & Marceau, E. (2006). On a risk model with dependence between interclaim arrivals and claim sizes. Scandinavian Actuarial Journal 2006, 265–285.
  • Constantinescu, C., Dai, S., Ni, W. & Palmowski, Z. (2016). Ruin probabilities with dependence on the number of claims within a fixed time window. Risks 4, 1–23.
  • Dickson, D. C. M. (2005). Insurance risk and ruin. International Series on Actuarial Science. Cambridge: Cambridge University Press.
  • Juan, L., Jiancheng, X. & Yijun, H. (2010). On the expected discounted penalty function in a Markov-dependent risk model with constant dividend barrier. Acta Mathematica Scientia 30, 1481–1491.
  • Kou, S. G. & Wang, H. (2003). First passage times of a jump diffusion process. Advances in Applied Probability 35, 504–531.
  • Kyprianou, A. (2013). Gerber-Shiu risk theory. EAA Series. Cham: Springer International Publishing.
  • Labbe, C. & Sendova, K. P. (2009). The expected discounted penalty function under a risk model with stochastic income. Applied Mathematics and Computation 215, 1852–1867.
  • Li, Z. & Sendova, K. P. (2015). On a ruin model with both interclaim times and premiums depending on claim sizes. Scandinavian Actuarial Journal 2015, 245–265.
  • Perry, D., Stadje, W. & Zacks, S. (2002). First-exit times for compound Poisson processes for some types of positive and negative jumps. Stochastic Models 18, 139–157.
  • Rolski, T., Schmidli, H., Schmidt, V. & Teugels, J. (2009). Stochastic processes for insurance and finance. Wiley Series in Probability and Statistics. Chichester: Wiley.
  • Shi, Y., Liu, P. & Zhang, C. (2013). On the compound Poisson risk model with dependence and a threshold dividend strategy. Statistics & Probability Letters 83, 1998–2006.
  • Temnov, G. (2004). Risk process with random income. Journal of Mathematical Sciences 123, 3780–3794.
  • Yin, C., Wen, Y., Zong, Z. & Shen, Y. (2014). The first passage time problem for mixed-exponential jump processes with applications in insurance and finance. Abstract and Applied Analysis 2014, 1–9.
  • Yu, W. & Huang, Y. (2015). A dependent insurance risk model with surrender and investment under the thinning process. Mathematical Problems in Engineering 2015, 1–8.
  • Zacks, S. (2007). First exit times for ordinary and compound Poisson processes with non-linear boundaries. Methodology and Computing in Applied Probability 9, 359–375.
  • Zhang, Z. & Yang, H. (2010). On a risk model with stochastic premiums income and dependence between income and loss. Journal of Computational and Applied Mathematics 234, 44–57.
  • Zhang, Z., Yang, H. & Li, S. (2010). The perturbed compound Poisson risk model with two-sided jumps. Journal of Computational and Applied Mathematics 233, 1773–1784.
  • Zhou, M. & Cai, J. (2009). A perturbed risk model with dependence between premium rates and claim sizes. Insurance: Mathematics and Economics 45, 382–392.
  • Zou, W., Gao, J.-W. & Xie, J.-H. (2014). On the expected discounted penalty function and optimal dividend strategy for a risk model with random incomes and interclaim-dependent claim sizes. Journal of Computational and Applied Mathematics 255, 270–281.

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