To offer or not to offer? The optimal value-insured strategy for crowdsourced delivery platforms

•The optimal value-insured strategy for crowdsourced delivery platforms is studied.•The optimal insurance scheme is explored by comparing three insurance scenarios.•CDPs’ value-insured strategy depends on couriers’ sensitivity to the declared value.•The reinsurance scheme or the fixed-fee scheme can generate the highest CDP’s profit.•Offering value-insured service is not always beneficial to stakeholders.