Optimal combined dividend and reinsurance policies under interest rate in Lévy markets

Sivuyile W. Mgobhozi and Eriyoti Chikodza

International Journal of Mathematics in Operational Research, 2017, vol. 10, issue 1, 69-83

Abstract: A combined dividend and risk control problem is presented and investigated in this paper. The risk of the insurance firm is controlled by using a proportional reinsurance policy. It is considered that the evolution of the cash reserves of the firm is driven by a generalised Itô-Lévy process. The surplus cash reserves earn interest at a constant rate. The objective of the firm is to maximise the total expected discounted dividends paid out to share holders. The situation is modelled as an impulse-classical control problem. We manage to construct the value function and the optimal impulse control. The existence and uniqueness of an optimal classical control is proved.

Keywords: quasi-variational inequality; impulse control; optimal stopping; dividend policy; reinsurance policy; interest rates; Levy markets; risk control; insurance industry; cash reserves; modelling. (search for similar items in EconPapers)
Date: 2017
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