Mean–variance asset–liability management: Cointegrated assets and insurance liability

► Consider the mean–variance ALM for an insurer investing in cointegrated assets. ► The insurer has random insurance claims during the investment period. ► The problem is solved by generalizing the approach in Lim (2005). ► The optimal control is obtained in explicit and closed-form formulas. ► Nume...

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Bibliographic Details
Published in:European journal of operational research Vol. 223; no. 3; pp. 785 - 793
Main Authors: Chiu, Mei Choi, Wong, Hoi Ying
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 16.12.2012
Elsevier
Elsevier Sequoia S.A
Subjects:
Applied sciences
Asset liability management
Cointegration
Exact sciences and technology
Exact solutions
Firm modelling
Inference from stochastic processes; time series analysis
Insurance
Insurance companies
Liability
Management
Markets
Mathematical models
Mathematics
Mean–variance portfolio theory
Operational research and scientific management
Operational research. Management science
Optimization algorithms
Policies
Portfolio management
Portfolio theory
Probability and statistics
Sciences and techniques of general use
Statistics
Studies
Terminals
Asset–liability management
Cointegration
Mean–variance portfolio theory
Asset and liability Management
Asset-liability management
Empirical method
Time series
Mean-variance portfolio theory
Financial management
Continuous time
Financial market
Modeling
Poisson process
Marketing
Exact solution
Brownian motion
Protest
Uncertain system
Insurance
Incomplete market
Error correction
Portfolio management
Investment
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:► Consider the mean–variance ALM for an insurer investing in cointegrated assets. ► The insurer has random insurance claims during the investment period. ► The problem is solved by generalizing the approach in Lim (2005). ► The optimal control is obtained in explicit and closed-form formulas. ► Numerical examples show that cointegration is important to ALM. The cointegration of major financial markets around the globe is well evidenced with strong empirical support. This paper considers the continuous-time mean–variance (MV) asset–liability management (ALM) problem for an insurer investing in an incomplete financial market with cointegrated assets. The number of trading assets is allowed to be less than the number of Brownian motions spanning the market. The insurer also faces the risk of paying uncertain insurance claims during the investment period. We assume that the cointegration market follows the diffusion limit of the error-correction model for cointegrated time series. Using the Markowitz (1952) MV portfolio criterion, we consider the insurer’s problem of minimizing variance in the terminal wealth, given an expected terminal wealth subject to interim random liability payments following a compound Poisson process. We generalize the technique developed by Lim (2005) to tackle this problem. The particular structure of cointegration enables us to solve the ALM problem completely in the sense that the solutions of the continuous-time portfolio policy and efficient frontier are obtained as explicit and closed-form formulas.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2012.07.009