Optimal Consumption, Leisure and Job Choice under Inflationary Environment

The optimal job choice,consumption and portfolio decision-making of economic agents under inflationary environment for a continuous infinite time are studied.The agent’s preference is characterized by the Cobb-Douglas utility function with two variables of consumption and leisure.The economic agent invests in three kinds of assets:risk-free bonds,inflation index bonds and risky assets.The agent has two kinds of working conditions:One is the work with high income and little leisure time,and the other is the work with low income and much leisure time.Firstly,the real wealth process after inflation discount is derived by using Itôformula.Then,based on the expected utility maximization standard under any working state,martingale method is adopted to obtain the closed form solution of optimal job choice,consumption and portfolio decision-making.Finally,the effects of wealth and inflation volatility on the optimal consumption and portfolio strategies are quantitatively analyzed by numerical simulation with given parameters.