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

Author

Listed:
  • Søren Asmussen

    (Department of Mathematics, Aarhus University, 8000 Aarhus, Denmark)

  • Bent Jesper Christensen

    (Department of Economics and Business Economics and the Dale T. Mortensen Centre, Aarhus University, 8210 Aarhus, Denmark)

  • Julie Thøgersen

    (Department of Mathematics, Aarhus University, 8000 Aarhus, Denmark)

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.

Suggested Citation

  • Søren Asmussen & Bent Jesper Christensen & Julie Thøgersen, 2019. "Stackelberg Equilibrium Premium Strategies for Push-Pull Competition in a Non-Life Insurance Market with Product Differentiation," Risks, MDPI, vol. 7(2), pages 1-23, May.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:2:p:49-:d:227500
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    References listed on IDEAS

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