Say I'm in the business of trading forward contracts. So at some point in time, I look at the markets, and determine a number of trades I could make. For each trade, I know the profit I expect to make, and the maturity date.

However, I can't make all the trades, because I only have finite capital (sad times). Even if I could make all the trades with the capital I have, it's possible that tomorrow I'll find new trades I can't make because all the capital is invested. So by making a good trade today I may miss the opportunity of making an even better trade tomorrow. The amount of available capital also varies over time, as the futures mature.

This looks like an interesting optimisation problem, so I suppose it's been exhaustively studied. But I've googled around and searched this site and came up empty, I believe because I lack the right vocabulary to describe the problem in the same way practitioners of the relevant discipline do.

So any pointers would be appreciated - both relevant articles / papers / books, or even if this is a well-known problem with a well-known name so I can be more successful with my research.

  • 2
    $\begingroup$ I think you need to specify what you want to maximize. If it's total expected return, then it looks like a variant of knapsack. $\endgroup$
    – LazyCat
    Jun 20, 2018 at 15:09
  • $\begingroup$ Thanks, will look into that. Not 100% sure about the metrics but total expected return sounds about right. $\endgroup$
    – ggambetta
    Jun 21, 2018 at 14:26


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