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- Title
Stackelberg Equilibrium Premium Strategies for Push-Pull Competition in a Non-Life Insurance Market with Product Differentiation.
- Authors
Asmussen, Søren; Christensen, Bent Jesper; Thøgersen, Julie
- 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.
- Subjects
PRODUCT differentiation; DIFFERENTIAL games; EQUILIBRIUM; INSURANCE; INSURANCE companies
- Publication
Risks, 2019, Vol 7, Issue 2, p49
- ISSN
2227-9091
- Publication type
Article
- DOI
10.3390/risks7020049