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An extension of Paulsen-Gjessing's risk model with stochastic return on investments

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  • Chuancun Yin
  • Yuzhen Wen

Abstract

We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model and then find the integro-differential equations satisfied by the Gerber-Shiu functions as well as the expected discounted penalty functions at ruin caused by a claim or by oscillation; We also study the dividend problem for the threshold and barrier strategies, the moments and moment-generating function of the total discounted dividends until ruin are discussed. Some examples are given for special cases.

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  • Chuancun Yin & Yuzhen Wen, 2013. "An extension of Paulsen-Gjessing's risk model with stochastic return on investments," Papers 1302.6757, arXiv.org.
    • Handle: RePEc:arx:papers:1302.6757
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    References listed on IDEAS

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    1. Paulsen, Jostein, 1998. "Ruin theory with compounding assets -- a survey," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 3-16, May.
    2. Jun Cai & Chengming Xu, 2006. "On The Decomposition Of The Ruin Probability For A Jump-Diffusion Surplus Process Compounded By A Geometric Brownian Motion," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 120-129.
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    4. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    5. Wan, Ning, 2007. "Dividend payments with a threshold strategy in the compound Poisson risk model perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 509-523, May.
    6. Jostein Paulsen, 2008. "Ruin models with investment income," Papers 0806.4125, arXiv.org, revised Dec 2008.
    7. Paulsen, Jostein & Gjessing, Hakon K., 1997. "Optimal choice of dividend barriers for a risk process with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 20(3), pages 215-223, October.
    8. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400.
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    10. Paulsen, Jostein & Kasozi, Juma & Steigen, Andreas, 2005. "A numerical method to find the probability of ultimate ruin in the classical risk model with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 399-420, June.
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    12. Wang, Guojing & Wu, Rong, 2008. "The expected discounted penalty function for the perturbed compound Poisson risk process with constant interest," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 59-64, February.
    13. Yang, Hailiang & Zhang, Lihong, 2005. "Optimal investment for insurer with jump-diffusion risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 615-634, December.
    14. Chuancun Yin & Chunwei Wang, 2010. "The Perturbed Compound Poisson Risk Process with Investment and Debit Interest," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 391-413, September.
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    Cited by:

    1. Yin, Chuancun & Wen, Yuzhen, 2013. "Optimal dividend problem with a terminal value for spectrally positive Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 769-773.
    2. Dan Zhu & Ming Zhou & Chuancun Yin, 2023. "Finite-Time Ruin Probabilities of Bidimensional Risk Models with Correlated Brownian Motions," Mathematics, MDPI, vol. 11(12), pages 1-18, June.
    3. Aleksandr Tarasyev & Ilya Krivenko & Maria Pecherkina & Tatiana Kashina, 2016. "Simulation of the Investment Attractiveness of Science in a Region," Economy of region, Centre for Economic Security, Institute of Economics of Ural Branch of Russian Academy of Sciences, vol. 1(1), pages 303-314.
    4. Chuancun Yin & Kam Chuen Yuen, 2014. "Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs," Papers 1409.0407, arXiv.org.
    5. Junxia Ma & Qiuling Fei & Fan Guo & Weili Xiong, 2019. "Variational Bayesian Iterative Estimation Algorithm for Linear Difference Equation Systems," Mathematics, MDPI, vol. 7(12), pages 1-16, November.

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