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

Authors: Sivuyile W. Mgobhozi; Eriyoti Chikodza

Addresses: School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, 4000, South Africa ' Department of Mathematics and Computer Science, Great Zimbabwe University, P.O. Box 1235, Masvingo, Zimbabwe

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.

DOI: 10.1504/IJMOR.2017.080745

International Journal of Mathematics in Operational Research, 2017 Vol.10 No.1, pp.69 - 83

Available online: 07 Nov 2016

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