Insurance companies, depending on the company and the line of business, will aim to make both an underwriting profit and an investment profit.
If it is a particularly high premium line, and especially if there is a lot of competition, it's more likely that the underwriting profit will be kept minimal or even negative, as the investment profit is so much more lucrative. This is common in the car insurance lines of business, for example.
For retail insurers there are a lot of moving parts here, and they will often not hold much of the final risk, so can't make money from investment anyway. For example, the retailer (sometimes an underwriting agency) may be underwritten by some bigger insurer.
That insurer may have a quota share arrangement with another insurer (I'll take 10% of the risk, you take 90%) with a corresponding premium share.
At each level reinsurance is bought, sometimes on the whole portfolio of risks and sometimes on particular classes of risk or specifc policies, and the costs associated with the reinsurance are priced into the retail premium.
Additionally, when working in an intermediated market with brokers, there are often credit terms of up to 90 days where no payments are made. Anecdotally, it does seem like some brokers do make a large amount of their money on this float.
Adding it all together, there are two main numbers to track from an underwriting profit point of view - your loss ratio (claims incurred / earned premiums, often extended to include projections for future claims and premium for future insured periods) and your combined operating ratio (COR) which includes expenses.
There will be a loss ratio at which a line of business becomes profitable, and final premiums are often calculated by taking the expected losses and grossing up by this loss ratio. For individual accounts it might literally be that simple - "over the last 5 years this account has averaged claims of $100,000 a year, we need a 60% loss ratio so the premium should be $166,667." If there are extra reinsurance costs you might add those, and you might also add a loading for large infrequent losses that aren't captured in your underlying loss ratio (and another loading for catastrophes, a level above that).
The combined ratio needs to be under 100% to be 'underwriting profitable'. I've seen CORs as high as 105-110%, but typically those portfolios were being very closely monitored/remediated/exited. If there is a strong market the COR is allowed to drift higher, but when the market tightens so does the COR.