scholarly journals COMPARISON OF MEAN VARIANCE LIKE STRATEGIES FOR OPTIMAL ASSET ALLOCATION PROBLEMS

2012 ◽  
Vol 15 (02) ◽  
pp. 1250014 ◽  
Author(s):  
J. WANG ◽  
P. A. FORSYTH
Keyword(s):  
Asset Allocation ◽  
Optimal Investment ◽  
Quadratic Variation ◽  
Investment Policy ◽  
Investment Policies ◽  
Efficient Frontiers ◽  
Dynamic Investment ◽  
Optimal Dynamic ◽  
Hamilton Jacobi Bellman ◽  
Mean Variance

We determine the optimal dynamic investment policy for a mean quadratic variation objective function by numerical solution of a nonlinear Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). We compare the efficient frontiers and optimal investment policies for three mean variance like strategies: pre-commitment mean variance, time-consistent mean variance, and mean quadratic variation, assuming realistic investment constraints (e.g. no bankruptcy, finite shorting, borrowing). When the investment policy is constrained, the efficient frontiers for all three objective functions are similar, but the optimal policies are quite different.

Dynamic mean variance asset allocation: Tests for robustness

2017 ◽  
Vol 04 (02n03) ◽  
pp. 1750021 ◽  
Author(s):  
Peter A. Forsyth ◽  
Kenneth R. Vetzal
Keyword(s):  
Asset Allocation ◽  
Stock Index ◽  
Dynamic Asset Allocation ◽  
Constant Weight ◽  
Terminal Wealth ◽  
Optimal Dynamic ◽  
Yearly Maximum ◽  
Hamilton Jacobi Bellman ◽  
Equity Index ◽  
Mean Variance

We consider a portfolio consisting of a risk-free bond and an equity index which follows a jump diffusion process. Parameters for the inflation-adjusted return of the stock index and the risk-free bond are determined by examining 89 years of data. The optimal dynamic asset allocation strategy for a long-term pre-commitment mean variance (MV) investor is determined by numerically solving a Hamilton–Jacobi–Bellman partial integro-differential equation. The MV strategy is mathematically equivalent to minimizing the quadratic shortfall of the target terminal wealth. We incorporate realistic constraints on the strategy: discrete rebalancing (yearly), maximum leverage, and no trading if insolvent. Extensive synthetic market tests and resampled backtests of historical data indicate that the multi-period MV strategy achieves approximately the same expected terminal wealth as a constant weight strategy, but with much smaller variance and probability of shortfall.

scholarly journals Optimal reinsurance and investment strategies for an insurer under monotone mean-variance criterion

2021 ◽  
Author(s):  
Bohan Li ◽  
Junyi Guo
Keyword(s):  
Optimal Strategy ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Capital Asset Pricing ◽  
Investment Strategies ◽  
Asset Pricing Model ◽  
Optimal Value ◽  
Hamilton Jacobi Bellman ◽  
Zero Sum ◽  
Mean Variance

This paper considers the optimal investment-reinsurance problem under the monotone mean-variance preference. The monotone mean-variance preference is a monotone version of the classical mean-variance preference. First of all, we reformulate the original problem as a zero-sum stochastic differential game. Secondly, the optimal strategy and the optimal value function for the monotone mean-variance problem are derived by the approach of dynamic programming and the Hamilton-Jacobi-Bellman-Isaacs equation. Thirdly, the efficient frontier is obtained and it is proved that the optimal strategy is an efficient strategy. Finally, the continuous-time monotone capital asset pricing model is derived.

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

2014 ◽  
Vol 56 (1) ◽  
pp. 66-90 ◽  
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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