The writer of a put option is hopeful that the:

The statement that the writer of a put option is hopeful that the market value is greater than the strike price of the underlying security at expiration reflects the understanding of how put options function. A put option gives the holder the right to sell the underlying asset at a specified strike price before expiration. When the market value of the underlying security is greater than the strike price, the put option becomes less likely to be exercised, as the holder would be better off selling the security at the higher market price rather than at the lower strike price.

For the writer of the put option, this scenario is advantageous. If the put option is not exercised, the writer retains the premium received from selling the option, thus benefiting from the situation. The goal of the writer is to profit from selling put options by hoping that the market conditions will lead to non-exercise of the option, which happens when the security's market value is above the strike price.

Understanding this dynamic is crucial for grasping options trading strategies and the risks and rewards associated with them.