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The Impact of Negative Interest Rates on Optimal Capital Injections

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  • Julia Eisenberg
  • Paul Kruhner

Abstract

In the present paper, we investigate the optimal capital injection behaviour of an insurance company if the interest rate is allowed to become negative. The surplus process of the considered insurance entity is assumed to follow a Brownian motion with drift. The changes in the interest rate are described via a Markov-switching process. It turns out that in times with a positive rate, it is optimal to inject capital only if the company becomes insolvent. However, if the rate is negative it might be optimal to hold a strictly positive reserve. We establish an algorithm for finding the value function and the optimal strategy, which is proved to be of barrier type. Using the iteration argument, we show that the value function solves the Hamilton--Jacobi--Bellman equation, corresponding to the problem.

Suggested Citation

  • Julia Eisenberg & Paul Kruhner, 2016. "The Impact of Negative Interest Rates on Optimal Capital Injections," Papers 1612.06654, arXiv.org.
    • Handle: RePEc:arx:papers:1612.06654
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    References listed on IDEAS

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    1. Zhu, Jinxia & Yang, Hailiang, 2008. "Ruin theory for a Markov regime-switching model under a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 311-318, February.
    2. Zhengjun Jiang & Martijn Pistorius, 2008. "On perpetual American put valuation and first-passage in a regime-switching model with jumps," Finance and Stochastics, Springer, vol. 12(3), pages 331-355, July.
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    5. Z. Jiang & M. R. Pistorius, 2008. "On perpetual American put valuation and first-passage in a regime-switching model with jumps," Papers 0803.2302, arXiv.org.
    6. Nie, Ciyu & Dickson, David C. M. & Li, Shuanming, 2011. "Minimizing the ruin probability through capital injections," Annals of Actuarial Science, Cambridge University Press, vol. 5(2), pages 195-209, September.
    7. Zhengjun Jiang & Martijn Pistorius, 2012. "Optimal dividend distribution under Markov regime switching," Finance and Stochastics, Springer, vol. 16(3), pages 449-476, July.
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