In this study, we investigate the information-based dynamic strategic decision makings in consumption, investment and life insurance purchase for a household with two consecutive generations.  A continuous-time model featuring the time-varying information-processing ability of the economic agent is considered. Specifically, we consider the situation where the decision makers cannot observe the states perfectly due to the impact of rational inattention, and they can only observe a noisy signal containing imperfect information about the states. The economic agent can dynamically change the information channel capacity of the private information to adjust the estimation accuracy. Closed-form solutions for value functions and optimal rules are obtained for before and after the death of the wage earner by adopting dynamic programming principle coupled with Hamilton-Jacobi-Bellman (HJB) equations. Finally, numerical studies are provided to illustrate the economic implications of the solutions.