考虑模型不确定的TBP养老金的鲁棒最优投资策略研究

以目标收益养老金计划(TBP)模型研究鲁棒最优投资问题, 其中养老金管理者对模型参数不确定带来的风险是模糊风险厌恶的. 养老金管理者为规避风险和增加收益将投资于无风险资产和风险资产. 考虑连续时间情形, 假设养老金计划参保人的缴费是确定的, 而参保人的收益给付是确定目标收益给付, 资金账户的收益风险由不同代际的参保人共同承担, 同时考虑随机工资及其与金融市场的相关性. 以参保人退休后养老金给付偏离目标的风险和代际之间风险分担的组合最小化为投资决策目标, 并采用指数函数的形式描述实际给付与目标给付的偏离, 利用随机最优控制方法, 建立相应的HJB方程并求解得到最优投资收益策略和最优给付策略的解析解. 通过数值示例分析了模型参数对最优投资和最优给付策略的影响.

Robust Optimal Investment Strategy under TBP Pension Model with Model Uncertainty

Pension managers, who worry about uncertainty in model parameters, investigate a robust optimal investment problem under the Target Benefit Plan (the TBP) model. The pension fund is invested in both a risk-free asset and a risky asset, in order to avoid market risk. In continuous time, the contribution of a person who participates in a pension plan is certain, while the pension payments are defined target benefit payments, and the income risk of capital account is shared between different generations. We consider the stochastic salary rates and the correlation between salary movements and market fluctuations, then we establish the dynamic model of collective account. In the frame of the model uncertainty, we derive HJB equation and closed-form solutions of the optimal investment strategy and benefit adjustment policy by using the stochastic optimal control approach in exponential target form, which minimizes the combination of benefit risk(in terms of deviating from the target) and intergenerational transfers. Finally, we illustrate the effects of model parameters on optimal investment strategy and benefit adjustment policy by numerical examples.