Nash equilibrium premium strategies for push–pull competition in a frictional non-life insurance market

TY - JOUR

T1 - Nash equilibrium premium strategies for push–pull competition in a frictional non-life insurance market

AU - Asmussen, Søren

AU - Christensen, Bent Jesper

AU - Thøgersen, Julie

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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)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 ∗ ,p 2 ∗ 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.

AB - 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)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 ∗ ,p 2 ∗ 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.

KW - Beta distribution

KW - Diffusion approximation

KW - Exit problem

KW - Market friction

KW - Nash equilibrium

KW - Saddle point

KW - Stochastic differential game

UR - http://www.scopus.com/inward/record.url?scp=85064945585&partnerID=8YFLogxK

U2 - 10.1016/j.insmatheco.2019.02.002

DO - 10.1016/j.insmatheco.2019.02.002

M3 - Journal article

AN - SCOPUS:85064945585

SN - 0167-6687

VL - 87

SP - 92

EP - 100

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

ER -