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Erscheinungsjahr: 
2019
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[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 7 [Issue:] 2 [Article No.:] 49 [Publisher:] MDPI [Place:] Basel [Year:] 2019 [Pages:] 1-20
Verlag: 
MDPI, Basel
Zusammenfassung: 
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)&#x2212;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.
Schlagwörter: 
Stochastic differential game
Product differentiation
Adverse selection
Stackelberg equilibrium
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