Challenges in stock market app development often include handling real-time data, ensuring security, and creating a scalable architecture. These challenges can be effectively addressed by leveraging AWS services in the trading application development process. For example, AWS Lambda can manage real-time events, ensuring that the stock trading app is always updated with the latest market data. Amazon Cognito can handle secure sign-up and sign-in, providing a secure environment for users. Lastly, the scalability provided by AWS's serverless architecture ensures that the trading app can handle high volumes of data and traffic, making it a reliable tool for stock trading.