Optimal asset allocation for pension funds under mortality risk during the accumulation and decumulation phases

In a financial market with one riskless asset and n risky assets whose prices are lognormal, we solve in a closed form the problem of a pension fund maximizing the expected CRRA utility of its surplus till the (stochastic) death time of a representative agent. We consider a unique asset allocation problem for both accumulation and decumulation phases. The optimal investment in the risky assets must decrease during the first phase and increase during the second one. We accordingly suggest it is not optimal to manage the two phases separately, and outsourcing of allocation decisions should be avoided in both phases. JEL: G23, G11 MSC 2000: 62P05, 91B28, 91B30, 91B70, 93E20     

Optimal assets allocation and benefit outgo policies of DC pension plan with compulsory conversion claims

In this paper, we study optimal asset allocation and benefit outgo policies of DC (defined contribution) pension plan. We extend He and Liang model (2013a,b) to describe dynamics of individual fund scale during distribution period. The fund scale is affected by investment return, benefit outgo and mortality credit. The management of the pension plan controls the asset allocation and benefit outgo policies to achieve the objective of pension members. The goal of the management is to minimize accumulated deviations between the actual benefit outgo and a pre-set target during the whole distribution period. The performance function (criterion) is the weighted average of the square and linear deviations to express more penalty on negative deviation than positive deviation. Using HJB (Hamilton–Jacobi–Bellman) equations and variational inequality methods, the closed-forms of the optimal policies are derived. The counterintuitive effect of the optimal proportion allocated in the risky asset with respect to the fund scale is also derived, and the optimal benefit outgo has the form of the spread method. Moreover, we use Monte Carlo Methods (MCM) to analyze economic behaviors of the optimal asset allocation and benefit outgo policies.     

Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework

This paper investigates an optimal investment strategy of DC pension plan in a stochastic interest rate and stochastic volatility framework. We apply an affine model including the Cox–Ingersoll–Ross (CIR) model and the Vasicek mode to characterize the interest rate while the stock price is given by the Heston’s stochastic volatility (SV) model. The pension manager can invest in cash, bond and stock in the financial market. Thus, the wealth of the pension fund is influenced by the financial risks in the market and the stochastic contribution from the fund participant. The goal of the fund manager is, coping with the contribution rate, to maximize the expectation of the constant relative risk aversion (CRRA) utility of the terminal value of the pension fund over a guarantee which serves as an annuity after retirement. We first transform the problem into a single investment problem, then derive an explicit solution via the stochastic programming method. Finally, the numerical analysis is given to show the impact of financial parameters on the optimal strategies.     

A stochastic programming model using an endogenously determined worst case risk measure for dynamic asset allocation

We present a new approach to asset allocation with transaction costs. A multiperiod stochastic linear programming model is developed where the risk is based on the worst case payoff that is endogenously determined by the model that balances expected return and risk. Utilizing portfolio protection and dynamic hedging, an investment portfolio similar to an option-like payoff structure on the initial investment portfolio is characterized. The relative changes in the expected terminal wealth, worst case payoff, and risk aversion, are studied theoretically and illustrated using a numerical example. This model dominates a static mean-variance model when the optimal portfolios are evaluated by the Sharpe ratio. Received: August 15, 1999 / Accepted: October 1, 2000?Published online December 15, 2000     

Risky asset allocation and consumption rule in the presence of background risk and insurance markets

This study examines joint decisions regarding risky asset allocation and consumption rate for a representative agent in the presence of background risk and insurance markets. Contrary to the conclusion of the “mutual fund separation theorem”, we show that the optimal risky asset mix will reflect an agent’s risk attitude as long as background risk is not independent of investment risk. This result can, however, be used to solve the “riskyasset allocation puzzle”. We also unveil that optimal insurance to shift background risk is determined through establishing a hedging portfolio against investment risk and is an arrangement maintaining the balance between growth and volatility of expected consumption. Because the optimal insurance we obtain generally leads to a smoother consumption path, it may plausibly explain the “equity premium puzzle” in the financial literature.     

A smoothing method for solving portfolio optimization with CVaR and applications in allocation of generation asset

This paper focuses on the computation issue of portfolio optimization with scenario-based CVaR. According to the semismoothness of the studied models, a smoothing technology is considered, and a smoothing SQP algorithm then is presented. The global convergence of the algorithm is established. Numerical examples arising from the allocation of generation assets in power markets are done. The computation efficiency between the proposed method and the linear programming (LP) method is compared. Numerical results show that the performance of the new approach is very good. The remarkable characteristic of the new method is threefold. First, the dimension of smoothing models for portfolio optimization with scenario-based CVaR is low and is independent of the number of samples. Second, the smoothing models retain the convexity of original portfolio optimization problems. Third, the complicated smoothing model that maximizes the profit under the CVaR constraint can be reduced to an ordinary optimization model equivalently. All of these show the advantage of the new method to improve the computation efficiency for solving portfolio optimization problems with CVaR measure.