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Stackelberg Equilibrium Premium Strategies for Push-Pull Competition in a Non-Life Insurance Market with Product Differentiation

1
Department of Mathematics, Aarhus University, 8000 Aarhus, Denmark
2
Department of Economics and Business Economics and the Dale T. Mortensen Centre, Aarhus University, 8210 Aarhus, Denmark
*
Author to whom correspondence should be addressed.
Risks 2019, 7(2), 49; https://doi.org/10.3390/risks7020049
Received: 16 January 2019 / Revised: 12 April 2019 / Accepted: 14 April 2019 / Published: 1 May 2019
(This article belongs to the Special Issue Recent Development in Actuarial Science and Related Fields)
Two insurance companies I 1 , I 2 with reserves R 1 ( t ) , R 2 ( t ) compete for customers, such that in a suitable differential game the smaller company I 2 with R 2 ( 0 ) < R 1 ( 0 ) aims at minimizing R 1 ( t ) R 2 ( t ) by using the premium p 2 as control and the larger I 1 at maximizing by using p 1 . Deductibles K 1 , K 2 are fixed but may be different. If K 1 > K 2 and I 2 is the leader choosing its premium first, conditions for Stackelberg equilibrium are established. For gamma-distributed rates of claim arrivals, explicit equilibrium premiums are obtained, and shown to depend on the running reserve difference. The analysis is based on the diffusion approximation to a standard Cramér-Lundberg risk process extended to allow investment in a risk-free asset. View Full-Text
Keywords: Stochastic differential game; Product differentiation; Adverse selection; Stackelberg equilibrium Stochastic differential game; Product differentiation; Adverse selection; Stackelberg equilibrium
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Asmussen, S.; Christensen, B.J.; Thøgersen, J. Stackelberg Equilibrium Premium Strategies for Push-Pull Competition in a Non-Life Insurance Market with Product Differentiation. Risks 2019, 7, 49.

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