Continuous-Time Mean-Variance Asset-Liability Management with Hidden Markovian Regime Switching

This paper considers a continuous-time mean-variance asset-liability management problem with incompletely observable information. An investor can only observe the prices of the asset and liability and the dynamics of the unobservable states of the underlying financial market is described by a hidden Markovian chain. The price of the risky asset is assumed to be governed by a hidden Markovian regime switching geometric Brownian motion and the liability is assumed to follow a hidden Markovian regime switching Brownian motion with drift, respectively. The appreciation rates of the risky asset and the liability are modulated by the hidden Markovian chain. By using the separation principle, the filtering-estimation problem and the mean-variance asset-liability management problem are discussed. The explicit expressions for the optimal asset-liability management strategy and the mean-variance efficient frontier are determined by using the stochastic maximum principle.

[1]  Michael U. Dothan,et al.  Equilibrium Interest Rates and Multiperiod Bonds in a Partially Observable Economy , 1986 .

[2]  Jiaqin Wei,et al.  Markowitz’s mean–variance asset–liability management with regime switching: A time-consistent approach , 2013 .

[3]  Duan Li,et al.  Asset and liability management under a continuous-time mean–variance optimization framework , 2006 .

[4]  J. Detemple.  Further results on asset pricing with incomplete information , 1991 .

[5]  Duan Li,et al.  Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation , 2000 .

[6]  Hailiang Yang,et al.  Markowitz's Mean-Variance Asset–Liability Management with Regime Switching: A Multi-Period Model , 2011 .

[7]  Shu-yi Xie,et al.  Continuous-time mean–variance portfolio selection with liability and regime switching , 2009 .

[8]  Yong Li,et al.  Continuous-time mean–variance asset–liability management with endogenous liabilities ☆ , 2013 .

[9]  William F. Sharpe,et al.  Liabilities— A New Approach , 1990 .

[10]  J. Detemple.  Asset Pricing in a Production Economy with Incomplete Information , 1986 .

[11]  Markus Leippold,et al.  A Geometric Approach to Multiperiod Mean Variance Optimization of Assets and Liabilities , 2002 .

[12]  Süleyman Özekici,et al.  Portfolio selection with imperfect information: A hidden Markov model , 2011 .

[13]  Zhongfei Li,et al.  Multi-period portfolio selection for asset-liability management with uncertain investment horizon , 2008 .

[14]  X. Zhou,et al.  Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework , 2000 .

[15]  Hailiang Yang,et al.  Markowitz’s mean-variance asset-liability management with regime switching: A continuous-time model , 2008 .

[16]  R. Elliott,et al.  On mean-variance portfolio selection under a hidden Markovian regime-switching model , 2010 .

[17]  H. Müller,et al.  Efficient Portfolios in the Asset Liability Context , 1995, ASTIN Bulletin.

[18]  Gerard Gennotte.  Optimal Portfolio Choice Under Incomplete Information , 1986 .

[19]  P. Samuelson.  Asset allocation could be dangerous to your health , 1990 .

[20]  Abel Cadenillas,et al.  EXPLICIT SOLUTIONS OF CONSUMPTION‐INVESTMENT PROBLEMS IN FINANCIAL MARKETS WITH REGIME SWITCHING , 2009 .

[21]  Shouyang Wang,et al.  Continuous-time portfolio selection with liability: Mean–variance model and stochastic LQ approach , 2008 .