How to approach this multi label classification problem and what will be its accuracy metric?
As with any data science problem: Approach the problem by first exploring the data and then trying the simplest solution that you think might just work, to some extent.

To explore the data, look at the distributions of all the features. Are they at all helpful to identifying the segments? How many trades do you have in the segments, are the classes balanced (more or less similar counts in all classes)? If not, you need to be careful with a metric like accuracy and you may be better off using F1 score, for example.

For an algorithm, how about starting with a decision tree and taking it from there? You can use it as a baseline model to compare to the results of other experiments. For example more complex algorithms using trees like boosted trees or random forest, or neural networks.

The performance metric is often averaged across all classes, using a technique called “1 versus all”. For that you start with the first segment, like “equity”. You can use the model to identify “equity” or “not equity”, and calculate the F1 score for this task. Repeat for all other classes and average.