On reinsurance and investment for large insurance portfolios

We consider a problem of optimal reinsurance and investment for an insurance company whose surplus is governed by a linear diffusion. The company’s risk (and simultaneously its potential profit) is reduced through reinsurance, while in addition the company invests its surplus in a financial market....

Full description

Saved in:
Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2008-02, Vol.42 (1), p.434-444
Main Authors: Luo, Shangzhen, Taksar, Michael, Tsoi, Allanus
Format: Article
Language:English
Subjects:
Banking
Black–Scholes model
Bonds
Capital market
Hamilton–Jacobi–Bellman equation
Insurance industry
Investment policy
Investments
Model testing
Modelling
Portfolio management
Probability
Proportional reinsurance
Reinsurance
Ruin probability
Stochastic control
Stochastic control theory
Stochastic models
Stochastic processes
Studies
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:We consider a problem of optimal reinsurance and investment for an insurance company whose surplus is governed by a linear diffusion. The company’s risk (and simultaneously its potential profit) is reduced through reinsurance, while in addition the company invests its surplus in a financial market. Our main goal is to find an optimal reinsurance–investment policy which minimizes the probability of ruin. More specifically, in this paper we consider the case of proportional reinsurance, and investment in a Black–Scholes market with one risk-free asset (bond, or bank account) and one risky asset (stock). We apply stochastic control theory to solve this problem. It transpires that the qualitative nature of the solution depends significantly on the interplay between the exogenous parameters and the constraints that we impose on the investment, such as the presence or absence of shortselling and/or borrowing. In each case we solve the corresponding Hamilton–Jacobi–Bellman equation and find a closed-form expression for the minimal ruin probability as well as the optimal reinsurance–investment policy.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2007.04.002