22 mathematical modeling contest 22 contest C

Digital analog idea sharing <– Male z Number Any reply to get the whole network idea

forecast + planning
2022 year MCM problem C: Trading strategies

Answer each question ：
● Develop a model , The model is based only on the price before that date (up to today) , Provide the best every
Daily trading strategy . According to your model and strategy , stay 2021 year 9 month 10 Japan , The original 1000 USD investment
How much is the asset value ?
Here is another key point , This is very clear , Only based on the price before that date (up totoday), in other words , For example 2017 year 9 month 10 Japan , There's data 、 Only to 2017 year 9 month 9 Japan , Then we need to make a prediction , You need to predict 2017 year 9 month 10 What is the trend of the meeting , Then see how to trade according to your forecast trend 、 Not from a God's point of view , I already know 9 month 10 What is the trend of Japan , And then buy and sell . therefore , This obviously involves a prediction model , This is also typical 、 Grey prediction model 、 Time series analysis model ,BP Neural network model . also LSTM Neural networks are good models for prediction . Then we have to predict the next day , To develop a planning model .
● Provide evidence that your model gives the best strategy .
Here we can give a disturbance to our trading strategy , Then look at the disturbance 、 Whether the transaction amount appears rose , Or investigate the difference between the forecast model and the actual value . If you use neural network and other methods, you can constantly repair Positive difference , Adjust the parameters , To minimize the difference ．
● Determine the sensitivity of the strategy to transaction costs . How transaction costs affect strategy and outcomes ？
This is for the above a％ Make an investigation , If a Fluctuate within a certain range , Smaller we will be more Trade frequently , Getting bigger will reduce the number of transactions , to a Some other values , Examine the impact on trading strategies influence .
● Share your strategy in a two page memo 、 Models and results are communicated to traders .
Flash point analysis ： This question is a typical prediction class ＋ Planning problems 、 The flash point can be started from two aspects Predictive aspects , Choose more accurate prediction models and tools , Adjust parameters, etc 、 meanwhile 、 From a thousand to financial investment , Risk is also a factor that must be considered , It is suggested to add risk analysis , In order to achieve more The results of beauty show the aspects of planning , After the objective function and constraints are given , How to do it faster Convergence is the thinking direction of planning , Such as greedy algorithm 、 Such as particle swarm optimization 、 Shoal of fish 、 Birds, etc , this Some of our series of intelligent algorithms have talked about , You can learn Some related theories , Code and results We can help to realize , You just need to write down the model theory and the model building part clearly ．

---- Reference for other ideas ：

analysis : This problem requires some machine learning algorithms , Especially the algorithms related to time series , such as ARIMA Algorithm
etc. . You can refer to some relevant knowledge of quantitative analysis . Generally, this kind of problem has two goals , One is the most effective investment
Dahua , The other is the lowest value at risk , The mathematical model can be established according to these two goals .
Add picture comments , No more than 140 word （ Optional ）
chart 1 : The daily price of gold , Dollars per troy ounce . source . London Bullion Market Association ,9/11/2021
Of
Add picture comments , No more than 140 word （ Optional ）
chart 2: Bitcoin daily price 、 US $per bitcoin . source . NASDAQ ,9/11/2021
requirement :

A trader asked you to develop a model , The model uses only the past flow of daily prices to date to determine daily deliveries
Should I buy 、 Holding or selling assets in its portfolio .
You will 2016 year 11 month 9 Japanese 1000 The dollar starts . You will use a five-year trading period , from 2016 year 11 month 9
Easy to 2021 year 9 month 9 Japan . On every trading day , Traders will have a One consists of cash 、 An investment consisting of gold and bitcoin
Combine [C, G, B], In US dollars 、 Troy ounce and bitmarket . The initial state is [1000, 0]. Every deal ( Buy
Or for sale ) The Commission is% of the transaction amount a%. hypothesis e gold =1%,a The currency =2 road . There is no cost to holding assets .
Please note that , Bitcoin can be traded every day , But gold only trades on the opening day , This is reflected in the pricing data file
LBMA One GQED.csv and BCHAIN One MKRRU.csV in . Your model should take into account this trading schedule .
To develop your model , You can only use the data in the two spreadsheets provided .LBMA:=GOLD.csv and .
BCHAIN One MKPRU.csv.

This model needs to use only the past flow of daily prices so far to determine whether daily traders should buy in 、 Hold or
Sell assets in their portfolio . So we need to use time series algorithm to predict the future . Only when you predict
by ” To make reasonable investment in asset planning . In the follow-up, we will predict the time series of the given data set ,
Will give the code and some related charts .
Be careful , The portfolio mentioned in the title [Q6, B], The units used vary , So when carrying out various operations ,
You need to check the unit ( dollar 、 Troy ounces and bitcoin ) convert < Then we can carry out the following operations . It should be noted that , transformation
You need to convert according to the price of the day . During operation , Commission also needs to be considered . According to the topic analysis ,
There are generally four operations , Namely :
1 Buying gold with cash ( The Commission is 1%) 2 Redeem gold ( The Commission is 1%) 3 Buy bitcoin in cash ( The Commission is 2%) 4 Sell bitcoin .《 The Commission is 2%)
among , Bitcoin can be traded every day , But gold only trades on the opening day ( Trading day ). All the trading rules here
Should follow American standards , Never follow Chinese standards ( dog's head , Bitcoin trading is illegal in China ,
Please note that )
subject
1 Develop a model , Give the best daily trading strategy based only on the price data as of that date . Use your models and strategies
A little , The original 1000 Dollars invested in 20215 year 9 month 9 What is the value of a day ?
analysis : please - - Be sure to read the attachment first 1, Dataset analysis , Read the attachment first 1 Look at the first - - Ask for ideas and you will understand .

The first question is to build a model , Through a reasonable daily trading strategy , To make 2021 year 9 month 9 Daily value is the highest .
Be careful : Don't make short-term investments , Unless the subsequent forecast value is high to a certain extent . Because there is a commission , I don't recommend
Make frequent transactions . Bitcoin has a large rise and fall , So try to use short-term trading , And gold fluctuates less , therefore
It is better to adopt medium and long-term transactions .
In the attachment 1 Written in , Three mathematical models need to be established : Investment risk model 、 Bull bear market judgment model 、 Time series prediction
) Model . The investment risk model is behind the bull bear market model , In this way, the indicators of bull and bear market can be used . In the attachment 2 To daosun °
The best yellow The way gold and bitcoin are traded .

Be careful :
1 Data preprocessing is required at the beginning of model establishment , At least the values need to be normalized .
2 The first two models use evaluation methods ( Each indicator needs to be weighted ), Consider the choice of indicators , from 20 Select the appropriate indicator from multiple indicators ( If our team wrote , Then it is likely to repeat , So the best thing is for everyone to choose ), Then add appropriate weight . In the follow-up thinking , There will be all the ideas mentioned . Code and visualization in , In the code there , The weights are set equally , When I use it, I get it according to my own algorithm
The weight of , Just modify the corresponding part of the code .
3 The investment risk model gets floating point data 、 The scope is 0-1、 The bull and bear market judgment model gets 0 perhaps 1, Fang
Method is to use evaluation method first （ Do not use analytic hierarchy process - Direct black drawing with digital analog method ）( The method is not the only way to get the weight ), Then set up - - Thresholds ( Set a reasonable
value , If it is greater than a certain value, it is a bull market , Less than is a bear market )
4 Time series prediction model , A classic model is ARIMA Of course, other prediction models can also be used , as long as
You can get the corresponding indicators , matter “
~5 The attachment 1 Medium 20 Multi index is just a temporary thought , For specific indicator information, please see the attachment 1 Oh ,. attach
1 Data set analysis and processing see my signature , Click on the business card below . It is very, very important for subsequent problem solving .

After these three models are completed , According to the original index and the index obtained by the model , Quantitative evaluation methods such as entropy weight method are used to solve ( Analytic hierarchy process is strongly deprecated )