We take a dynamic perspective on insurance markets under adverseselection and study a generalized Rothschildand Stiglitz model where agents may differ with respect to theaccidental probability and their expenditure levels incase an accident occurs. We investigate the nature of dynamicinsurance contracts by considering both conditionaland unconditional dynamic contracts. An unconditional dynamiccontract has insurance companies offeringcontracts where the terms of the contract depend on time, but not onthe occurrence of past accidents. Conditionaldynamic contracts make the actual contract also depend on individualpast performance (like in car insurances). Weinvestigate whether allowing insurance companies to offer dynamicinsurance contracts results in Pareto-improvements over static contracts. Our main results are as follows.When agents only differ in their accidentalexpenditures, then dynamic insurance contracts yield a welfareimprovement only if dynamic contracts areconditional on past performance. When, however, agents' expendituresdiffer just a little bit dynamic insurancecontracts are strictly Pareto improving even for unconditionaldynamic contracts.