Maximum value of arbitrage
The question is at least poorly worded, since it does not specify $k \leq n$ or require a simple cycle. So any positive-value arbitrage cycle can be "pumped" to generate a cycle with unbounded positive value.

If we add the requirement that the cycle is simple, then finding the simple cycle with the maximum product of the weights is equivalent to finding the simple cycle with the maximum sum of the logarithms of the weights, which is indeed the NP-hard Longest Simple Cycle problem.

Usually, these arbitrage questions ask to find a cycle with positive return, if one exists. This can be done by negating the logarithms of the weights and checking for negative cycles. This question asks for the best cycle, though.