This paper develops a dynamic framework for optimal household decisions regarding consumption, portfolio allocation, and insurance in the presence of jump-diffusion risk, imperfect market correlation, and insurance premium loading. Unlike models that address these choices in isolation, we jointly model financial assets, durable goods, and insurable shocks to capture the nonlinear interactions shaped by volatility, insurance costs, and macroeconomic policy. Simulation results show that insurance availability stabilizes consumption and investment, while higher premiums or incomplete markets trigger precautionary behavior — lowering consumption, reducing exposure to risky assets, and increasing reliance on durables for self-insurance. Importantly, the relationship between insurance cost and portfolio risk is nonmonotonic: as insurance becomes more expensive, households initially increase financial risk-taking, but eventually retreat from it when volatility and perceived background risk rise. Rising interest rates amplify these effects by heightening the demand for liquidity and further displacing both insurance uptake and investment. These findings offer policy-relevant insights into how financial fragility and insurance frictions jointly influence household behavior under uncertainty.
Perera et al. (Thu,) studied this question.