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An extension of Paulsen–Gjessing’s risk model with stochastic return on investments

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  • Yin, Chuancun
  • Wen, Yuzhen

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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  • Yin, Chuancun & Wen, Yuzhen, 2013. "An extension of Paulsen–Gjessing’s risk model with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 469-476.
    • Handle: RePEc:eee:insuma:v:52:y:2013:i:3:p:469-476
    DOI: 10.1016/j.insmatheco.2013.02.014
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    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. 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.
    5. 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.

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