Mean–variance asset–liability management: Cointegrated assets and insurance liability
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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- Cerchi, Marlene & Havenner, Arthur, 1988. "Cointegration and stock prices : The random walk on wall street revisited," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 333-346.
- Baillie, Richard T & Bollerslev, Tim, 1989. " Common Stochastic Trends in a System of Exchange Rates," Journal of Finance, American Finance Association, vol. 44(1), pages 167-81, March.
- Hipp, Christian & Plum, Michael, 2000. "Optimal investment for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 215-228, October.
- Engle, Robert & Granger, Clive, 2015.
"Co-integration and error correction: Representation, estimation, and testing,"
Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
- Chiu, Mei Choi & Wong, Hoi Ying, 2011. "Mean-variance portfolio selection of cointegrated assets," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1369-1385, August.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- Wang, J. & Forsyth, P.A., 2011. "Continuous time mean variance asset allocation: A time-consistent strategy," European Journal of Operational Research, Elsevier, vol. 209(2), pages 184-201, March.
- Serletis, Apostolos, 1994. "A cointegration analysis of petroleum futures prices," Energy Economics, Elsevier, vol. 16(2), pages 93-97, April.
- Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
- Duan, Jin-Chuan & Pliska, Stanley R., 2004. "Option valuation with co-integrated asset prices," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 727-754, January.
- Jorion, Philippe & Sweeney, Richard J., 1996. "Mean reversion in real exchange rates: evidence and implications for forecasting," Journal of International Money and Finance, Elsevier, vol. 15(4), pages 535-550, August.
- Sweeney, Richard J., 2006. "Mean Reversion in G-10 Nominal Exchange Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 41(03), pages 685-708, September.
- Duan Li & Wan-Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406.
- Taylor, Mark P & Tonks, Ian, 1989. "The Internationalisation of Stock Markets and the Abolition of U.K. Exchange Control," The Review of Economics and Statistics, MIT Press, vol. 71(2), pages 332-36, May.
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