Optimal Consumption and Investment Problem Incorporating Housing and Life Insurance Decisions: The Continuous Time Case

This study considers the optimal consumption-investment-insurance problem incorporating housing decisions of a household when interest rates and labor income are stochastic. Under the complete market assumption, we derive the closed-form solution of the optimal insurance demand, portfolio choice, and housing consumption. We calibrate the model using data from the financial market of Taiwan. We find that the insurer's pricing strategy has a significant impact on the household's consumption pattern. Specifically, additional loading in insurance premium allows the life-cycle model to produce hump-shaped consumptions of both perishable goods and housing. Loading also creates an unfair background risk to households. However, we only find a small portfolio risk reduction, because households optimally choose a large coverage to mitigate the mortality exposure. This suggests empirical background risk studies overestimate the risk reduction when insurance is available.