Quant Interview Practice Questions

A confused trader is trying to navigate the market's ups and downs. Imagine their portfolio value as performing a symmetric random walk on a multi-dimensional integer lattice. In a 2-dimensional market (only two assets), it is known that the trader will, with probability 1, return to their starting portfolio value at some point in the future (recurrence). Now, consider a more complex market with three assets. What can you say about the probability of the trader's portfolio value returning to its