# 2022MCM-C
**2022年数模美赛C题代码** [[paper](paper.pdf)]
- 整体工作
![2022MCM-C/our_work.jpg at master · dreaming-qin/2022MCM-C (github.com)](img/our_work.jpg)
- 为什么用LSTM,简述结构?
- 序列预测...
- 隐状态 [h, c] ,遗忘门 f ,输入门 i ,输出门o。
- 模型的输出取决于为 上一时刻的隐状态 和 输入x 。
- 损失函数取均方误差。
- 简述VaR思想?
- 假设 k 时刻的数据分布为D(k),**第k天的预测价格** 和 **第k-1天的价格** 进行**差分**,得到一个序列,将其**排序**,就得到了 **利润分布 ** D(k)。
- 假设所取数据天数为 len ,置信度为 c ,则第 len*(1-c) 天的价格就是 VaR 的值,表示有 c 的概率下一天会赚取或亏损这么多钱。
- 用 VaR/pk 就是**损失率 LR** 。
- 如何买卖?
- **PI**:LSTM自回归预测未来15天的**最大价格**,rk为当天的**真实价格**,PI相当于一个利润比率。
$$
PI(k)=\frac {max(p_1, p_2, ..., p_{15})-r_k}{r_k}
$$
且价格最大的这一天就是要卖出的天dm。
- **RI**:利用 LR ,相当于一个损失比率。
$$
RI(k)=(d_m-d_k) · LR
$$
- **F**:综合考虑PI和RI。rho取决于交易成本。beta是动态变化的,因为持有的资本越多,投入就越多,风险越大,就越要给RI更多的权重,F>0时就可以考虑交易。
$$
F=\beta · PI(k) + (1-\beta) · RI(k) - \rho
$$
- 算出黄金和比特币的 Fg, Fb ,进入有限状态自动机的状态。
- 优先卖比特币。
- 周末不交易。
- ...各种状态,比较复杂。(待补充)
- 如何评价模型?
- 根据交易策略,获得一个**总资产 M** 的走势曲线。
![2022MCM-C/result_1_new.jpg at master · dreaming-qin/2022MCM-C (github.com)](img/result_1_new.jpg)
- 对比几个模型:
1. 三次指数平滑:(待补充)
2. LSTM-only:只预测,若能盈利就买卖。
3. VaR-only:只看风险,若能盈利就买卖。
4. LSTM + VaR:综合。
- **滑动窗口机制**,窗口大小80天,滑动步数20天。
- 几个指标:
1. **FAV** (Final Asset Value) 最终利润,越大越好
2. **DR** (Down Risk) 下行风险,越小越好
对于黄金,用利润的平均值 * 天数,得到一个总利润,加上资产总额 M ,得到黄金预计资产 EG
对于比特币也是,得到 EB
然后加权,得到**总预计资产E**,然后求得DR
$$
E = \lambda · EG + (1-\lambda)·EB \\
DR = \sqrt{\frac{\sum min(0, E - M)^2}{n}}
$$
3. **MD** (Max Drawdown) 最大回撤,越小越好
从窗口中间划分,取得左半侧的最大值Mmax,和右半侧的最小值Mmin
$$
MD=\frac {M_{min}}{M_{max}}
$$
![2022MCM-C/problem_3_MD_FAV.jpg at master · dreaming-qin/2022MCM-C (github.com)](img/problem_3_MD_FAV.jpg)
- 通过实验,探索了交易成本对rho的影响,从而对交易策略和最终利润的影响。
- 灵敏性分析:beta对模型的影响,不稳定性先下降后上升,取0.6最合适。
![2022MCM-C/sensitivity.jpg at master · dreaming-qin/2022MCM-C (github.com)](img/sensitivity.jpg)
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