Intertemporal Optimal Portfolio Choice In The Long Run And Its Application In The Evaluation Of Target Date Fund Within Risky Income,Information Cost And Short Sales

This paper examines optimal portfolio choice within risky labor income,retire-ment and shadow costs of incomplete information and short sales.The optimal al-location to stocks is larger for employed investors than for retired investors within idiosyncratic labor income risk and incomplete information.Investors' willingness to save is increased when increasing idiosyncratic labor income risk in the presence of in-complete information.Hence,they reduce their stock portfolio allocation towards the level of retired investors.The presence of a positive correlation between labor income and stock returns reduces stockholdings below the level of retired investors within shadow costs of incomplete information.Our results generalize previous finding in models with complete information and no short sales constraints.The most distinguished character of the Target Date Funds is the glide path,which represents the proportion of risky assets allocated to the portfolio and the proportion will decrease along with the time until the retirement.We will apply stochastic optimal control model to find the optimal glide path.We assume that labor income is risky and follow the geometric Brownian motion.There are two periods to be discussed:employment state and retirement state.The main difference between the two periods is whether there is labor income or not,therefore,the model of employment state including risky labor income will be more complicated.What's more,in our model we assume that there exists correlation between labor income and risky asset(stocks).It' s worthy to be discussed about the positive or negative correlation which has an influence on the optimal proportion of portfolio choice.After the discussion of optimal glide path,we introduce other factors and apply Analytic Hierarchy Process to get the weights,so as to obtain the total score and find the optimal Target Date Fund.We introduce other indicators including,for example,Sortino Ratio,Return,Fund managers,etc.Two methods are applied here,one is to score each factor,then apply AHP to get weights;the other is to apply AHP directly.We use two hierarchy rankings to get the final scores and compare the results of the two methods.In the end,we will carry on simulation of our optimal glide path and get the graph.We also analyze the sensitivity of main parameters based on our rules of two states and further verify out results.