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The impact of negative interest rates on optimal capital injections

Julia Eisenberg and Paul Krühner

Insurance: Mathematics and Economics, 2018, vol. 82, issue C, 1-10

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.

Keywords: Negative interest rate; Capital injections; Markov-switching; Optimal stochastic control; Hamilton–Jacobi–Bellman equation (search for similar items in EconPapers)
JEL-codes: C61 G22 (search for similar items in EconPapers)
Date: 2018
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Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

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