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Submodular Risk Allocation


  • Samim Ghamami

    () (Center for Risk Management Research, Department of Economics, University of California, Berkeley, California 94720)

  • Paul Glasserman

    () (Graduate School of Business, Columbia Business School, New York, New York 10027)


We analyze the optimal allocation of trades to portfolios when the cost associated with an allocation is proportional to each portfolio’s risk. Our investigation is motivated by changes in the over-the-counter derivatives markets, under which some contracts may be traded bilaterally or through central counterparties, splitting a set of trades into two or more portfolios. A derivatives dealer faces risk-based collateral and capital costs for each portfolio, and it seeks to minimize total margin requirements through its allocation of trades to portfolios. When margin requirements are submodular, the problem becomes a submodular intersection problem. Its dual provides per-trade margin attributions, and assigning trades to portfolios based on the lowest attributed costs yields an optimal allocation. As part of this investigation, we derive conditions under which standard deviation and other risk measures are submodular functions of sets of trades. We compare systemwide optimality with individually optimal allocations in a market with multiple dealers.

Suggested Citation

  • Samim Ghamami & Paul Glasserman, 2019. "Submodular Risk Allocation," Management Science, INFORMS, vol. 65(10), pages 4656-4675, October.
  • Handle: RePEc:inm:ormnsc:v:65:y:2019:i:10:p:4656-4675
    DOI: 10.1287/mnsc.2018.3156

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    References listed on IDEAS

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