Submodular Risk Allocation
研究了在交易成本与投资组合风险成正比时，如何将交易最优地分配到多个投资组合中，以最小化总保证金要求，并推导了标准差等风险测度成为次模函数的条件。
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. This paper was accepted by Yinyu Ye, optimization.