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

Søren Asmussen (), Bent Jesper Christensen () and Julie Thøgersen ()
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Søren Asmussen: Department of Mathematics, Aarhus University, 8000 Aarhus, Denmark
Julie Thøgersen: Department of Mathematics, Aarhus University, 8000 Aarhus, Denmark

Risks, 2019, vol. 7, issue 2, 1-23

Abstract: 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.

Keywords: Stochastic differential game; Product differentiation; Adverse selection; Stackelberg equilibrium (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 M2 M4 K2 (search for similar items in EconPapers)
Date: 2019
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