Nash equilibrium premium strategies for push-pull competition in a frictional non-life insurance market. (English) Zbl 1410.91255
Summary: Two insurance companies \(I_1\), \(I_2\) with reserves \(R_1(t)\), \(R_2(t)\) compete for customers, such that in a suitable stochastic 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 \(p_1\). The dependence of reserves on premia is derived by modelling the customer’s problem explicitly, accounting for market frictions \(V\), reflecting differences in cost of search and switching, information acquisition and processing, or preferences. Assuming \(V\) to be random across customers, the optimal simultaneous choice \(p_1^\ast\), \(p_2^\ast\) of premiums is derived and shown to provide a Nash equilibrium for beta distributed \(V\). The analysis is based on the diffusion approximation to a standard Cramér-Lundberg risk process extended to allow investment in a risk-free asset.
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 91A15 | Stochastic games, stochastic differential games |
| 60J75 | Jump processes (MSC2010) |
Keywords:
stochastic differential game; diffusion approximation; exit problem; market friction; Nash equilibrium; saddle point; beta distributionReferences:
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