查看“︁现金流匹配”︁的源代码

'''现金流匹配'''是一种[[套期保值]]过程，在该过程中，公司或个体将其现金流出（例如债务偿还）与其在给定时间范围内的现金流入相匹配。<ref>{{Cite web|title=Cash flow matching|url=https://www.washingtonpost.com/wp-srv/business/longterm/glossary/a_m/cash_flow_matching.htm|url-status=live|archive-url=https://web.archive.org/web/20121102185537/https://www.washingtonpost.com/wp-srv/business/longterm/glossary/a_m/cash_flow_matching.htm|archive-date=November 2, 2012|website=The Washington Post}}</ref>它是金融免疫策略的一个子集。<ref>{{Cite web|url=https://www.cfainstitute.org/en/membership/professional-development/refresher-readings/2020/liability-driven-index-based-strategies|title=Liability-Driven and Index-Based Strategies|website=CFA Institute|language=en-US|access-date=2020-03-16}}{{Dead link}}</ref>现金流匹配在固定收益养老金项目中很重要。<ref>{{Cite web|url=https://www.gsam.com/content/dam/gsam/pdfs/institutions/en/articles/pension-solutions/2020/Cash_Flow_Matching_Feb_2020_locked.pdf?sa=n&rd=n|title=Cash Flow Matching: The Next Phase of Pension Plan Management|last=|first=|date=February 2020|website=Goldman Sachs Asset Management|url-status=live|archive-url=https://web.archive.org/web/20220621213621/https://www.gsam.com/content/dam/gsam/pdfs/institutions/en/articles/pension-solutions/2020/Cash_Flow_Matching_Feb_2020_locked.pdf?sa=n&rd=n|archive-date=2022-06-21|access-date=}}</ref>
==用线性规划求解==
现金流匹配问题可使用线性规划求解。<ref>{{Cite book|last=Cornuéjols|first=Gérard|url=https://www.cambridge.org/us/academic/subjects/mathematics/mathematical-finance/optimization-methods-finance-2nd-edition?format=HB|title=Optimization Methods in Finance|last2=Peña|first2=Javier|last3=Tütüncü|first3=Reha|publisher=Cambridge University Press|year=2018|isbn=9781107056749|edition=2nd|location=Cambridge, UK|pages=35-37|access-date=2022-06-20|archive-date=2021-06-23|archive-url=https://web.archive.org/web/20210623213701/https://www.cambridge.org/us/academic/subjects/mathematics/mathematical-finance/optimization-methods-finance-2nd-edition?format=HB}}</ref>先假设我们有<math>j=1,...,n</math>这<math>n</math>个债券，这些债券在<math>t=1,...,T</math>这<math>T</math>个周期中产生现金流，但是在每个周期中分别存在需要偿还的负债<math>L_{1},...,L_{T}</math>需要偿还。假设债券<math>j</math>的初始价格为<math>p_{j}</math>，在周期<math>t</math>中可获得的现金流为<math>F_{tj}</math>。因此可以购买债券<math>x_{j}</math>在特定周期中获得盈余<math>s_{t}</math>，两者均为非负数，因此存在下列限制式：<math display="block">\begin{aligned}
\sum_{j=1}^{n}F_{1j}x_{j} - s_{1} &= L_{1} \\
\sum_{j=1}^{n}F_{tj}x_{j} + s_{t-1} - s_{t} &= L_{t}, \quad t = 2,...,T
\end{aligned}</math>

我们的目标是将购买债券的初始成本<math>p^{T}x</math>最小化，同时还要求每个周期中产生的收益不小于需要偿还的负债。因此可以构建以下线性规划问题：<math display="block">\min_{x,s} \; p^{T}x, \quad \text{s.t.} \; Fx + Rs = L, \; x,s\geq 0</math>其中在<math>F\in\mathbb{R}^{T\times n}</math>和<math>R\in\mathbb{R}^{T\times T}</math>需要：<math display="block">R_{t,t} = -1, \quad R_{t+1,t} = 1</math>

考虑到在购买债券时所涉及到的购买数量是离散的，因此可以使用[[整数规划|混合整数线性规划]]来构建此类问题。

==参考文献==
{{reflist}}

[[Category:现金流量]]
[[Category:公司金融]]
[[Category:金融衍生工具]]
[[Category:金融风险管理]]
[[Category:線性規劃]]