Mean-variance equilibrium asset-liability management strategy with cointegrated assets

2021 ◽  
Vol 62 ◽  
pp. 209-234
Author(s):  
Mei Choi Chiu
Keyword(s):  
Financial Market ◽  
Time Consistency ◽  
Time Inconsistency ◽  
Asset Liability Management ◽  
Risky Assets ◽  
Liability Management ◽  
Equilibrium Control ◽  
Management Problems ◽  
Hamilton Jacobi Bellman ◽  
Mean Variance

This paper investigates asset-liability management problems in a continuous-time economy. When the financial market consists of cointegrated risky assets, institutional investors attempt to make profit from the cointegration feature on the one hand, while on the other hand they need to maintain a stable surplus level, that is, the company’s wealth less its liability. Challenges occur when the liability is random and cannot be fully financed or hedged through the financial market. For mean–variance investors, an additional concern is the rational time-consistency issue, which ensures that a decision made in the future will not be restricted by the current surplus level. By putting all these factors together, this paper derives a closed-form feedback equilibrium control for time-consistent mean–variance asset-liability management problems with cointegrated risky assets. The solution is built upon the Hamilton–Jacobi–Bellman framework addressing time inconsistency. doi: 10.1017/S1446181120000164

MEAN–VARIANCE EQUILIBRIUM ASSET-LIABILITY MANAGEMENT STRATEGY WITH COINTEGRATED ASSETS

2020 ◽  
Vol 62 (2) ◽  
pp. 209-234
Author(s):  
MEI CHOI CHIU
Keyword(s):  
Financial Market ◽  
Time Consistency ◽  
Time Inconsistency ◽  
Asset Liability Management ◽  
Risky Assets ◽  
Liability Management ◽  
Equilibrium Control ◽  
Management Problems ◽  
Hamilton Jacobi Bellman ◽  
Mean Variance

AbstractThis paper investigates asset-liability management problems in a continuous-time economy. When the financial market consists of cointegrated risky assets, institutional investors attempt to make profit from the cointegration feature on the one hand, while on the other hand they need to maintain a stable surplus level, that is, the company’s wealth less its liability. Challenges occur when the liability is random and cannot be fully financed or hedged through the financial market. For mean–variance investors, an additional concern is the rational time-consistency issue, which ensures that a decision made in the future will not be restricted by the current surplus level. By putting all these factors together, this paper derives a closed-form feedback equilibrium control for time-consistent mean–variance asset-liability management problems with cointegrated risky assets. The solution is built upon the Hamilton–Jacobi–Bellman framework addressing time inconsistency.

scholarly journals Time Consistent Strategies for Mean-Variance Asset-Liability Management Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Hui-qiang Ma ◽  
Meng Wu ◽  
Nan-jing Huang
Keyword(s):  
Optimal Time ◽  
Investment Strategies ◽  
Asset Liability Management ◽  
Programming Technique ◽  
Liability Management ◽  
Management Problems ◽  
Time Diversification ◽  
Riskless Asset ◽  
Mean Variance ◽  
Variance Criterion

This paper studies the optimal time consistent investment strategies in multiperiod asset-liability management problems under mean-variance criterion. By applying time consistent model of Chen et al. (2013) and employing dynamic programming technique, we derive two-time consistent policies for asset-liability management problems in a market with and without a riskless asset, respectively. We show that the presence of liability does affect the optimal strategy. More specifically, liability leads a parallel shift of optimal time-consistent investment policy. Moreover, for an arbitrarily risk averse investor (under the variance criterion) with liability, the time-diversification effects could be ignored in a market with a riskless asset; however, it should be considered in a market without any riskless asset.

scholarly journals The Study of Mean-Variance Risky Asset Management with State-Dependent Risk Aversion under Regime Switching Market

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Shuang Li ◽  
Yu Yang ◽  
Yanli Zhou ◽  
Yonghong Wu ◽  
Xiangyu Ge
Keyword(s):  
Risk Aversion ◽  
Asset Management ◽  
Regime Switching ◽  
Asset Liability Management ◽  
Risky Assets ◽  
Liability Management ◽  
State Dependent ◽  
Optimal Value ◽  
Time Inconsistent ◽  
Mean Variance

How do investors require a distribution of the wealth among multiple risky assets while facing the risk of the uncontrollable payment for random liabilities? To cope with this problem, firstly, this paper explores the approach of asset-liability management under the state-dependent risk aversion with only risky assets, which has been considered under a continuous-time Markov regime-switching setting. Next, based on this realistic modelling, an extended Hamilton-Jacob-Bellman (HJB) system has been necessarily established for solving the optimization problem of asset-liability management. It has been derived closed-form analytical expressions applied in the time-inconsistent investment with optimal control theory to see that happens to the optimal value of the function. Ultimately, numerical examples presented with comparisons of the analytical results under different market conditions are exposed to analyse numerically the developed mean variance asset liability management strategy. We find that our proposed model can explain the financial phenomena more effectively and accurately.

scholarly journals ON TIME CONSISTENCY FOR MEAN-VARIANCE PORTFOLIO SELECTION

2020 ◽  
Vol 23 (06) ◽  
pp. 2050042 ◽  
Author(s):  
ELENA VIGNA
Keyword(s):  
Portfolio Selection ◽  
Optimal Strategy ◽  
Time Consistency ◽  
Time Inconsistency ◽  
Selection Problem ◽  
Portfolio Selection Problem ◽  
The Mean ◽  
Optimal Approach ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper addresses a comparison between different approaches to time inconsistency for the mean-variance portfolio selection problem. We define a suitable intertemporal preferences-driven reward and use it to compare three common approaches to time inconsistency for the mean-variance portfolio selection problem over [Formula: see text]: precommitment approach, consistent planning or game theoretical approach, and dynamically optimal approach. We prove that, while the precommitment strategy beats the other two strategies (that is a well-known obvious result), the consistent planning strategy dominates the dynamically optimal strategy until a time point [Formula: see text] and is dominated by the dynamically optimal strategy from [Formula: see text] onwards. Existence and uniqueness of the break even point [Formula: see text] is proven.

scholarly journals A Random Parameter Model for Continuous-Time Mean-Variance Asset-Liability Management

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Hui-qiang Ma ◽  
Meng Wu ◽  
Nan-jing Huang
Keyword(s):  
Continuous Time ◽  
Efficient Frontier ◽  
Random Parameter ◽  
Management Problem ◽  
Random Parameters ◽  
Asset Liability Management ◽  
Linear Quadratic ◽  
Liability Management ◽  
The Mean ◽  
Mean Variance

We consider a continuous-time mean-variance asset-liability management problem in a market with random market parameters; that is, interest rate, appreciation rates, and volatility rates are considered to be stochastic processes. By using the theories of stochastic linear-quadratic (LQ) optimal control and backward stochastic differential equations (BSDEs), we tackle this problem and derive optimal investment strategies as well as the mean-variance efficient frontier analytically in terms of the solution of BSDEs. We find that the efficient frontier is still a parabola in a market with random parameters. Comparing with the existing results, we also find that the liability does not affect the feasibility of the mean-variance portfolio selection problem. However, in an incomplete market with random parameters, the liability can not be fully hedged.

scholarly journals Optimal Reinsurance-Investment Problem under Mean-Variance Criterion with n Risky Assets

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Peng Yang
Keyword(s):  
Financial Market ◽  
Investment Strategy ◽  
Hjb Equation ◽  
Model Parameters ◽  
Optimal Reinsurance ◽  
Risky Assets ◽  
Terminal Wealth ◽  
Investment Problem ◽  
Mean Variance ◽  
Variance Criterion

Based on the mean-variance criterion, this paper investigates the continuous-time reinsurance and investment problem. The insurer’s surplus process is assumed to follow Cramér–Lundberg model. The insurer is allowed to purchase reinsurance for reducing claim risk. The reinsurance pattern that the insurer adopts is combining proportional and excess of loss reinsurance. In addition, the insurer can invest in financial market to increase his wealth. The financial market consists of one risk-free asset and n correlated risky assets. The objective is to minimize the variance of the terminal wealth under the given expected value of the terminal wealth. By applying the principle of dynamic programming, we establish a Hamilton–Jacobi–Bellman (HJB) equation. Furthermore, we derive the explicit solutions for the optimal reinsurance-investment strategy and the corresponding efficient frontier by solving the HJB equation. Finally, numerical examples are provided to illustrate how the optimal reinsurance-investment strategy changes with model parameters.

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