Stackelberg equilibrium premium strategies for push-pull competition in a non-life insurance market with product differentiation

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Abstract

Two insurance companies I1, 1 I2 with reserves R1(t), R2(t) compete for customers, such that in a suitable differential game the smaller company I2 with R2(0) < R1(0) aims at minimizing R1(t) &#x100000; R2(t) by using the premium p2 as control and the larger I1 at maximizing by using p1. Deductibles K1, K2 are fixed but may be different. If K1 > K2 and I2 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.
Original languageEnglish
Article number49
JournalRisks
Volume7
Issue2
DOIs
Publication statusPublished - May 2019

Keywords

  • Product differentiation
  • Stackelberg equilibrium
  • Stochastic differential game

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