We study the dynamics of microinsurance demand by risk‐averse agents who can borrow and lend subject to a liquidity constraint, and also perceive a risk of insurer default. Liquidity constraints and perceived insurer default both reduce the demand for insurance, possibly leading to nonparticipation. We also evaluate an alternative insurance design that allows agents to delay premium payment until the end of the insured period when income is realized and indemnities are paid. We show this alternative design increases insurance take‐up by relaxing the liquidity constraint and ameliorating concerns about insurer default. We also investigate the value of delayed premium payment, and the importance of the associated problem of reneging if the insured event does not occur, under a range of conditions.