Abstract
To maintain and increase household wealth, this study studies the optimal allocation ratio of household investment and consumption. When considering venture capital, it is assumed that the theoretical price of risky asset obeys the CEV model. Our goal was to maximize the expectation of household cumulative consumption and the discounted utility of terminal wealth and to solve the optimal consumption and investment ratio using the dynamic programming principle and HJB equation. Using logarithmic utility and isoelastic power utility function with residual utility, we get the analytical solution of the household investment‐consumption ratio by means of guessing and variable transformation. Finally, the influence of general parameters on the optimal ratio in the market is analyzed by numerical simulation and diagram, which is consistent with the description of actual situation. This study not only enriches portfolio theory but also provides investors with investment strategies.
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