A characterization of equilibrium strategies in continuous-time mean–variance problems for insurers

In this work, we study the equilibrium reinsurance/new business and investment strategy for mean–variance insurers with constant risk aversion. The insurers are allowed to purchase proportional reinsurance, acquire new business and invest in a financial market, where the surplus of the insurers is a...

Full description

Saved in:
Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2016-05, Vol.68, p.212-223
Main Authors: Alia, Ishak, Chighoub, Farid, Sohail, Ayesha
Format: Article
Language:English
Subjects:
Equilibrium
Equilibrium strategy
Forward–backward stochastic differential equation
Insurer
Investment–reinsurance strategy
Mean–variance criterion
Reinsurance
Risk aversion
Securities markets
Studies
Time inconsistency
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this work, we study the equilibrium reinsurance/new business and investment strategy for mean–variance insurers with constant risk aversion. The insurers are allowed to purchase proportional reinsurance, acquire new business and invest in a financial market, where the surplus of the insurers is assumed to follow a jump–diffusion model and the financial market consists of one riskless asset and a multiple risky assets whose price processes are driven by Poisson random measures and independent Brownian motions. By using a version of the stochastic maximum principle approach, we characterize the open loop equilibrium strategies via a stochastic system which consists of a flow of forward–backward stochastic differential equations (FBSDEs in short) and an equilibrium condition. Then by decoupling the flow of FSBDEs, an explicit representation of an equilibrium solution is derived as well as its corresponding objective function value.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2016.03.009