Optimal time-consistent portfolio and contribution selection for defined benefit pension schemes under mean–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.

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OPTIMAL TIME-CONSISTENT PORTFOLIO AND CONTRIBUTION SELECTION FOR DEFINED BENEFIT PENSION SCHEMES UNDER MEAN–VARIANCE CRITERION

The ANZIAM Journal ◽

10.1017/s1446181114000212 ◽

2014 ◽

Vol 56 (1) ◽

pp. 66-90 ◽

Cited By ~ 2

Author(s):

XIAOQING LIANG ◽

LIHUA BAI ◽

JUNYI GUO

Keyword(s):

Risk Aversion ◽

Asset Allocation ◽

Optimization Problems ◽

Realistic Model ◽

Optimal Time ◽

Pension Scheme ◽

Defined Benefit ◽

Special Cases ◽

Hamilton Jacobi Bellman ◽

Mean Variance

AbstractWe investigate two mean–variance optimization problems for a single cohort of workers in an accumulation phase of a defined benefit pension scheme. Since the mortality intensity evolves as a general Markov diffusion process, the liability is random. The fund manager aims to cover this uncertain liability via controlling the asset allocation strategy and the contribution rate. In order to have a more realistic model, we study the case when the risk aversion depends dynamically on current wealth. By solving an extended Hamilton–Jacobi–Bellman system, we obtain analytical solutions for the equilibrium strategies and value function which depend on both current wealth and mortality intensity. Moreover, results for the constant risk aversion are presented as special cases of our models.

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Dynamic Optimal Mean-Variance Investment with Mispricing in the Family of 4/2 Stochastic Volatility Models

Mathematics ◽

10.3390/math9182293 ◽

2021 ◽

Vol 9 (18) ◽

pp. 2293

Author(s):

Yumo Zhang

Keyword(s):

Stochastic Volatility ◽

Time Inconsistency ◽

Closed Form Expression ◽

Optimal Time ◽

Model Parameters ◽

Stochastic Volatility Models ◽

Volatility Models ◽

The Family ◽

Mean Variance ◽

Variance Criterion

This paper considers an optimal investment problem with mispricing in the family of 4/2 stochastic volatility models under mean–variance criterion. The financial market consists of a risk-free asset, a market index and a pair of mispriced stocks. By applying the linear–quadratic stochastic control theory and solving the corresponding Hamilton–Jacobi–Bellman equation, explicit expressions for the statically optimal (pre-commitment) strategy and the corresponding optimal value function are derived. Moreover, a necessary verification theorem was provided based on an assumption of the model parameters with the investment horizon. Due to the time-inconsistency under mean–variance criterion, we give a dynamic formulation of the problem and obtain the closed-form expression of the dynamically optimal (time-consistent) strategy. This strategy is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Results on the special case without mispricing are included. Finally, some numerical examples are given to illustrate the effects of model parameters on the efficient frontier and the difference between static and dynamic optimality.

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Greatest Good 2: Response to the Department for Work & Pensions Green Paper 'Security and Sustainability in Defined Benefit Pension Schemes'

SSRN Electronic Journal ◽

10.2139/ssrn.3610359 ◽

2017 ◽

Author(s):

David P. Blake ◽

Matthew Roy

Keyword(s):

Green Paper ◽

Defined Benefit ◽

Pension Schemes

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Continuous-time mean-variance portfolio selection with regime-switching financial market: Time-consistent solution

Random Operators and Stochastic Equations ◽

10.1515/rose-2020-2050 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Ishak Alia ◽

Farid Chighoub

Keyword(s):

Portfolio Selection ◽

Regime Switching ◽

Optimal Time ◽

Uniqueness Results ◽

State Dependent ◽

Consistent Solution ◽

Game Theoretic ◽

Markov Modulated ◽

Mean Variance Portfolio ◽

Mean Variance

Abstract This paper studies optimal time-consistent strategies for the mean-variance portfolio selection problem. Especially, we assume that the price processes of risky stocks are described by regime-switching SDEs. We consider a Markov-modulated state-dependent risk aversion and we formulate the problem in the game theoretic framework. Then, by solving a flow of forward-backward stochastic differential equations, an explicit representation as well as uniqueness results of an equilibrium solution are obtained.

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