Bajaj was in the city to attend a financial conclave organised by the Bengal Chamber of Commerce.
He said both the life and general insurance companies were well capitalised and its promoters remained committed.
Bajaj Allianz Life is among the most capital-efficient among private insurers with a solvency ratio of 608 per cent as on September 30, Bajaj said.
In addition, the insurance firm has a fund of Rs 2,348 crore beyond the solvency margin, which forms a part of shareholders' investments, he said. Bajaj Allianz Life posted a net profit of Rs 836 crore in FY17.
Solvency ratio in case of Bajaj Allianz General Insurance is 288 per cent as against the regulatory requirement of 150 per cent, as of September 30, Bajaj said. The firm's bottomline for FY17 stood at Rs 727.8 crore.
A number of insurance companies have launched initial public offering (IPO) in the past few months, including SBI Life Insurance, General Insurance Corp of India (GIC Re) and New India Assurance.
HDFC Standard Life Insurance's IPO is slated for November 7.
To a separate question on the Goods and Services Tax, Bajaj said benefits from the new tax regime would be seen in the next three to four quarters.