Under what circumstance can an insurer withdraw quoted terms once accepted in writing?

The correct choice highlights that an insurer can withdraw quoted terms once they have been accepted in writing if the basis of the risk has changed. This is rooted in the principle that the acceptance of an insurance proposal is based on the risk assessment that the insurer conducts at the time of quoting. If new information emerges that alters the understanding of the risk, such as a material change in the risk profile or the condition of the insured subject, the terms can no longer be upheld. This is essential as insurance underwriting relies heavily on accurate and complete information to determine fair pricing and coverage conditions.

This principle aims to protect insurers from unforeseen circumstances that could significantly affect their exposure or the viability of the policy they are issuing. In such cases, it is reasonable for an insurer to reassess the terms initially offered or to choose not to provide coverage at all, as the risk landscape has fundamentally shifted.

The other options do not adequately reflect the nuanced nature of risk assessment in underwriting practices. While market conditions and availability of cover can influence an insurer's strategies, they do not provide a valid reason for changing accepted terms post-acceptance based on a material change in risk. Therefore, the concept of changing terms hinges mainly on alterations in the risk itself.