The impact of negative interest rates on optimal capital injections



Eisenberg, J and Krühner, Paul
(2018) The impact of negative interest rates on optimal capital injections. Insurance: Mathematics and Economics, 82. 1 - 10.

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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.

Item Type: Article
Uncontrolled Keywords: Negative interest rate, Capital injections, Markov-switching, Optimal stochastic control, Hamilton-Jacobi-Bellman equation
Depositing User: Symplectic Admin
Date Deposited: 10 Dec 2018 11:12
Last Modified: 09 Jan 2021 04:32
DOI: 10.1016/j.insmatheco.2018.06.004
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3029727