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Submodular Risk Allocation

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  • 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)

Abstract

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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    File URL: https://doi.org/10.1287/mnsc.2018.3156
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    References listed on IDEAS

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    1. Duffie, Darrell & Scheicher, Martin & Vuillemey, Guillaume, 2015. "Central clearing and collateral demand," Journal of Financial Economics, Elsevier, vol. 116(2), pages 237-256.
    2. David Backus & Mikhail Chernov & Stanley Zin, 2014. "Sources of Entropy in Representative Agent Models," Journal of Finance, American Finance Association, vol. 69(1), pages 51-99, February.
    3. Nicholas Vause, 2010. "Counterparty risk and contract volumes in the credit default swap market," BIS Quarterly Review, Bank for International Settlements, December.
    4. Satoru Fujishige & Kiyohito Nagano, 2009. "A Structure Theory for the Parametric Submodular Intersection Problem," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 513-521, August.
    5. Paul Embrechts & Haiyan Liu & Tiantian Mao & Ruodu Wang, 2017. "Quantile-Based Risk Sharing with Heterogeneous Beliefs," Swiss Finance Institute Research Paper Series 17-65, Swiss Finance Institute, revised Jan 2018.
    6. M. Schneider & F. Lillo, 2019. "Cross-impact and no-dynamic-arbitrage," Quantitative Finance, Taylor & Francis Journals, vol. 19(1), pages 137-154, January.
    7. Dan A. Iancu & Nikolaos Trichakis, 2014. "Fairness and Efficiency in Multiportfolio Optimization," Operations Research, INFORMS, vol. 62(6), pages 1285-1301, December.
    8. Leif Andersen & Darrell Duffie & Yang Song, 2019. "Funding Value Adjustments," Journal of Finance, American Finance Association, vol. 74(1), pages 145-192, February.
    9. Ghamami, Samim & Glasserman, Paul, 2017. "Does OTC derivatives reform incentivize central clearing?," Journal of Financial Intermediation, Elsevier, vol. 32(C), pages 76-87.
    10. Miguel Lobo & Maryam Fazel & Stephen Boyd, 2007. "Portfolio optimization with linear and fixed transaction costs," Annals of Operations Research, Springer, vol. 152(1), pages 341-365, July.
    11. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    12. Sidanius, Che & Zikes, Filip, 2012. "Financial Stability Paper No 18: OTC derivatives reform and collateral demand impact," Bank of England Financial Stability Papers 18, Bank of England.
    13. Jianjun Gao & Duan Li, 2013. "Optimal Cardinality Constrained Portfolio Selection," Operations Research, INFORMS, vol. 61(3), pages 745-761, June.
    14. Satoru Fujishige, 1980. "Lexicographically Optimal Base of a Polymatroid with Respect to a Weight Vector," Mathematics of Operations Research, INFORMS, vol. 5(2), pages 186-196, May.
    15. Shoshana Anily & Moshe Haviv, 2007. "The Cost Allocation Problem for the First Order Interaction Joint Replenishment Model," Operations Research, INFORMS, vol. 55(2), pages 292-302, April.
    16. Jean-Pierre Aubin, 1981. "Cooperative Fuzzy Games," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 1-13, February.
    17. Justin A. Sirignano & Gerry Tsoukalas & Kay Giesecke, 2016. "Large-Scale Loan Portfolio Selection," Operations Research, INFORMS, vol. 64(6), pages 1239-1255, December.
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