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Stackelberg equilibrium premium strategies for push-pull competition in a non-life insurance market with product differentiation

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Stackelberg equilibrium premium strategies for push-pull competition in a non-life insurance market with product differentiation. / Asmussen, Søren; Christensen, Bent Jesper; Thøgersen, Julie.

I: Risks, Bind 7, Nr. 2, 49, 05.2019.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

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@article{a49e433651e44eb98e95dcd248e2cacd,
title = "Stackelberg equilibrium premium strategies for push-pull competition in a non-life insurance market with product differentiation",
abstract = "Two insurance companies I1, 1 I2 with reserves R1(t), R2(t) compete for customers, such that in a suitable differential game the smaller company I2 with R2(0) < R1(0) aims at minimizing R1(t) 􀀀 R2(t) by using the premium p2 as control and the larger I1 at maximizing by using p1. Deductibles K1, K2 are fixed but may be different. If K1 > K2 and I2 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 Cram{\'e}r-Lundberg risk process extended to allow investment in a risk-free asset.",
keywords = "Stochastic differential game, Product differentiation, Stackelberg equilibrium",
author = "S{\o}ren Asmussen and Christensen, {Bent Jesper} and Julie Th{\o}gersen",
year = "2019",
month = may,
doi = "/10.3390/risks7020049",
language = "English",
volume = "7",
journal = "Risks",
issn = "2227-9091",
publisher = "MDPI",
number = "2",

}

RIS

TY - JOUR

T1 - Stackelberg equilibrium premium strategies for push-pull competition in a non-life insurance market with product differentiation

AU - Asmussen, Søren

AU - Christensen, Bent Jesper

AU - Thøgersen, Julie

PY - 2019/5

Y1 - 2019/5

N2 - Two insurance companies I1, 1 I2 with reserves R1(t), R2(t) compete for customers, such that in a suitable differential game the smaller company I2 with R2(0) < R1(0) aims at minimizing R1(t) 􀀀 R2(t) by using the premium p2 as control and the larger I1 at maximizing by using p1. Deductibles K1, K2 are fixed but may be different. If K1 > K2 and I2 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.

AB - Two insurance companies I1, 1 I2 with reserves R1(t), R2(t) compete for customers, such that in a suitable differential game the smaller company I2 with R2(0) < R1(0) aims at minimizing R1(t) 􀀀 R2(t) by using the premium p2 as control and the larger I1 at maximizing by using p1. Deductibles K1, K2 are fixed but may be different. If K1 > K2 and I2 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.

KW - Stochastic differential game

KW - Product differentiation

KW - Stackelberg equilibrium

U2 - /10.3390/risks7020049

DO - /10.3390/risks7020049

M3 - Journal article

VL - 7

JO - Risks

JF - Risks

SN - 2227-9091

IS - 2

M1 - 49

ER -