Abstract
This paper is concerned with studying an optimal multi-period asset-liability mean-variance portfolio selection with probability constraints using mean-field formulation without embedding technique. We strictly derive its analytical optimal strategy and efficient frontier. Numerical examples shed light on efficiency and accuracy of our method when dealing with this class of multi-period non-separable mean-variance portfolio selection problems.
Highlights
Mean-variance portfolio selection refers to the design of optimal portfolios balancing gain with risk, which are in expressions of expectation and variance of the terminal return, respectively
We employ mean-filed formulation to successfully reformulate the nonseparable problem to a mean-field linear-quadratic stochastic control problem which can be solvable by the classical dynamic programming approach, and strictly derive analytical optimal strategy of this problem and its efficient frontier
The mean-variance model for multi-period asset and liability portfolio selection with probability constraints is to seek the best strategy, πt∗ = [(πt1)∗,∗, · · ·,∗], t = 0, 1, · · ·, T −1, which is the optimizer of the following stochastic optimal control problem
Summary
Mean-variance portfolio selection refers to the design of optimal portfolios balancing gain with risk, which are in expressions of expectation and variance of the terminal return, respectively. Mean-field formulation, multi-period portfolio selection, asset-liability management, probability constraints, optimal strategy. Chiu-Li [3] employed the stochastic optimal control theory to analytically solve the asset-liability management in a continuous time setting.
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