Submodular Risk Allocation

39 Pages Posted: 3 Aug 2017

See all articles by Samim Ghamami

Samim Ghamami

Securities and Exchange Commission (SEC); New York University (NYU); University of California, Berkeley - Center for Risk Management Research

Paul Glasserman

Columbia Business School

Date Written: August 1, 2017


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.

Keywords: OTC Derivatives Market, Central Clearing, Collateral, Capital, Submodularity, Optimization

JEL Classification: G10, G21, C60, C71

Suggested Citation

Ghamami, Samim and Glasserman, Paul, Submodular Risk Allocation (August 1, 2017). Columbia Business School Research Paper No. 17-79, Available at SSRN: or

Samim Ghamami (Contact Author)

Securities and Exchange Commission (SEC) ( email )

450 Fifth Street, NW
Washington, DC 20549-1105
United States

New York University (NYU) ( email )

Bobst Library, E-resource Acquisitions
20 Cooper Square 3rd Floor
New York, NY 10003-711
United States

University of California, Berkeley - Center for Risk Management Research ( email )

581 Evans Hall
Berkely, CA 94720
United States

Paul Glasserman

Columbia Business School ( email )

New York, NY
United States

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