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

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

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Two insurance companies I 1 , lolasalinas.com 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 click here in a risk-free asset.