When you are sorting by Assignee on your Kanban board, you will be able to view both Budget and Budget Allocated. If you are unable to see this section, be sure to turn on the 'Display Column Totals'.
The 'Budget' amounts show the aggregate 'Budget' amounts for all work items assigned to you.
'Budget Allocated' shows the aggregate amounts assigned for that individual — this includes work items assigned to that individual, and any work items that individual is involved in.