This study explores the optimal trajectory of life insurance demand, a crucial financial tool for managing mortality risk and ensuring economic security for family. Various factors, including mortality risk, wealth growth, interest rates, and policyholder preferences, influence insurance decisions. To analyze these dynamics, the study develops two mathematical models. The first is a single-period, state-dependent model that maximizes expected utility under budget constraints, concluding that individuals optimally purchase only partial insurance. To obtain the optimal time path of life insurance coverage, a life-cycle model was solved using optimal control theory. By maximizing expected lifetime utility from consumption and bequests within the wealth accumulation process, the second model derives the trajectory of life insurance demand. The results indicate that individuals with higher risk tolerance experience a greater growth rate in life insurance demand. This growth rate is also positively influenced by mortality rates, loading factors, and interest rates. Conversely, life insurance demand declines as wealth increases, supporting the notion that wealth acts as a substitute for life insurance. Additionally, a higher rate of time preference negatively impacts the growth rate of life insurance demand.
Ghadir Mahdavi (Tue,) studied this question.