Optimal Investment Problem For A Target Benefit Pension Plan With Exponential Target Form

Pension service finance is an important guarantee to deal with the future uncertainty and improve the quality of life of the elderly,which is of great significance to Chinese economic development and social stability.But demographic,financial fluctuations and rising life expectancy are threatening pension systems around the world.At present,the resonance,correlation and systemic risk among various financial markets are increasing,and the pension system should be set to deal with such risks in the capital market.Therefore,the research on hybrid pension has received more and more attention.Based on the current financial market,this paper takes economic and financial policies into account.In this paper,the hybrid pension plan we study is a collective pension,the most prominent feature of TBP(Target Benefit Pension)is that plan members bear all of the risks,however,these risks are shared among different generations of members(including on-the-job personnel,retirees and has yet to enter the members of the pension scheme)instead of being borne individually.The plan enables risk transfer and sharing among participants,so that subsidies among intergenerational members can maintain a stable level of benefit payments and maintain the sustainability of pension plans.Firstly,we investigate a robust optimal investment problem under the TBP model for pension managers,who worries about uncertainty in model parameters.Investors invest their assets with 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 that stochastic salary rates and the correlation between salary movements and market fluctuations,then we establish the dynamic model of collective account.Then,the constant elastic variance(CEV)model,which is more in line with the actual market requirements,is introduced into the research of pension fund investment.The risk asset price follows the CEV model,and the risk process faced by the insurer is Brown motion with drift.Thus we consider the optimal investment problem of target benefit pension with salary determination.In the model above,we derive HJB equation and closed-form solutions of the optimal investment strategy and benefit adjustment policy with using the stochastic optimal control approach in exponential target form,which minimize 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.