好奇看了下今年的美赛C题，是一道关于在考虑交易佣金情况的求解一个交易费率的最大化问题

1、原题（Trading Strategies）

（1）Background

Market traders buy and sell volatile assets frequently, with a goal to maximize their total return.
There is usually a commission for each purchase and sale. Two such assets are gold and bitcoin.

Source: London Bullion Market Association, 9/11/2021
数据源自纳斯达克

Source: NASDAQ, 9/11/2021

（2）Requirement

You have been asked by a trader to develop a model that uses only the past stream of daily prices
to date to determine each day if the trader should buy, hold, or sell their assets in their portfolio.
You will start with $1000 on 9/11/2016. You will use the five-year trading period, from
9/11/2016 to 9/10/2021. On each trading day, the trader will have a portfolio consisting of cash,
gold, and bitcoin [C, G, B] in U.S. dollars, troy ounces, and bitcoins, respectively. The initial
state is [1000, 0, 0]. The commission for each transaction (purchase or sale) costs α% of the
amount traded. Assume ${\alpha }_{gold}$ = 1% and ${\alpha }_{bitcoin}$ = 2%. There is no cost to hold an asset.

Note that bitcoin can be traded every day, but gold is only traded on days the market is open, as
reflected in the pricing data files LBMA-GOLD.csv and BCHAIN-MKPRU.csv. Your model
should account for this trading schedule.
To develop your model, you may only use the data in the two spreadsheets provided:
LBMA-GOLD.csv and BCHAIN-MKPRU.csv.

• Develop a model that gives the best daily trading strategy based only on price data up
  to that day. How much is the initial $1000 investment worth on 9/10/2021 using your
  model and strategy?
• Present evidence that your model provides the best strategy.
• Determine how sensitive the strategy is to transaction costs. How do transaction costs affect the strategy and results?
• Communicate your strategy, model, and results to the trader in a memorandum of at most two pages.
  Your PDF solution of no more than 25 total pages should include:
• One-page Summary Sheet.
• Table of Contents.
• Your complete solution.
• One- to two-page Memorandum.
• Reference List.
  Note: The MCM has a 25-page limit. All aspects of your submission count toward the 25-page
  limit (Summary Sheet, Table of Contents, Reference List, and any Appendices). You must cite
  the sources for your ideas, images, and any other materials used in your report.

（3）Attachments

THE TWO DATA FILES PROVIDED CONTAIN THE ONLY DATA YOU SHOULD USE
FOR THIS PROBLEM.

1. LBMA-GOLD.csv
2. BCHAIN-MKPRU.csv

（4）Data Descriptions

1. LBMA-GOLD.csv

• Date: The date in mm-dd-yyyy (month-day-year) format.
• USD (PM): The closing price of a troy ounce of gold in U.S. dollars on the indicated
  date.

2. BCHAIN-MKPRU.csv

• Date: The date in mm-dd-yyyy (month-day-year) format.
• Value: The price in U.S. dollars of a single bitcoin on the indicated date.

2、翻译(交易策略)&题意理解

（1） 问题背景

市场交易中投资价格波动的资产的目的是实现回报的最大化，买卖过程中会产生交易佣金，以上两种资产分别为黄金和比特币：
图见上文（2016~2021 5年期间两种投资标的日价格）

（2）要求

开发一个交易模型，模型仅能够使用迄今为止的每日价格来确定当天是否应该买入 平仓 或者清仓该类资产；

给到的交易场景：

• 交易时间：2016年9月11日~2021年9月10日；
• 交易最大持仓：1000美金
• 交易费率：黄金为1% 比特币为2%
• 可以只有的资产种类： 现金 黄金 比特币 [C,G,B],初始状态为[1000,0,0]
• 投资资产的交易特性：黄金：仅交易日交易（节假日不能亏），比特币：每日交易（每天都能亏）；
• 模型使用数据：只能用出题方给的数据；

要解决的问题&要求

• 开发一个交易模型，制定一个最有的交易策略，该策略在2021年9月10月资产价值是多少？
• 证明模型策略最佳；
• 探究策略的的敏感度，说明交易成本对策略与最终结果的影响
• 把策略、模型结果汇总为不超过2页的备忘录

常规的写作要求

• 页数不超过25
• 一页摘要
• 目录
• 完整的解决方案
• 备忘录
• 参考文献列表

（3）附件

黄金与比特币近5年（2016~2021）数据

1. LBMA-GOLD.csv
2. BCHAIN-MKPRU.csv

（4）数据说明

1. LBMA-GOLD.csv

• Date：mm-dd-yyyy（月-日-年）格式的日期。
• USD (PM)：一金衡盎司黄金在指定日期的美元收盘价。

2. BCHAIN-MKPRU.csv - Date：mm-dd-yyyy（月-日-年）
   格式的日期。

• Value：指定日期单个比特币的美元价格。