Analysis on the thinking of 2022 meisai C question

Topic translation ：

2022 MCM subject C: Trade strategy

background :

The market trader shall purchase and sell the shares , The goal is to maximize their total return . For every purchase and sale , There is often a return commission . The two cases are gold and bitcoin .

Your team was asked by traders to build a mathematical model , Use only the daily prices in the past , To determine whether traders should buy , hold , Or sell their shares .

2016 year II month 9 Japan , First you have 1000 dollar , You will have a five-year trading period , from 2016 year II month 9 The day is coming 2021 year 10 month 9 Japan . During the daily trading period , The trader will have an account , Including cash , gold , The currency . The initial state is [1000 , 0 , 0], Every trade （ Buy or sell ） The cost of is the amount of trade Of a%, among , Suppose gold and bitcoin a% Namely 1% and 2%. There is no cost to hold shares . Be careful , Bitcoin can be traded every day , But gold can only be traded when the market is open . Relevant data are reflected in the two annexes CSV In file . Your model should take into account such a trade plan .

To build your model , You can only use two of the attachments CSV The data in the file ： LBMA-GOLD.csvandBCHAIN-MKPRU.csv.

- Build a mathematical model , Based on the price data as of that day , Give the best strategy for daily trading . Use you Of Models and strategies , If it is the initial one 1000 Dollar investment , So in 2021 year 10 month 9 How much is it worth per day ？

・ Give evidence , Explain that your mathematical model can provide the best trade strategy .

・ Make sure your strategy is sensitive to trading prices , How trading prices affect your strategy and results ？

• In two pages , Communicate your strategy to traders , Models and results .

Yours PDF Solution （ The paper ） No more than 25 page , It should include :

・ One page summary page

• Catalog

・ Your complete solution

• 1~2 Page memo

・ reference

Be careful :MCM Yes 25 Page limit for pages , All parts of the thesis should not exceed 25 page . At the same time, you need to quote the pictures correctly , Literature, etc .

Thought analysis ：

1、 Problem analysis ：

The understanding of this topic is relatively simple , It is the analysis of investment strategy by using historical data , Only previous historical data can be used for each day's decision . Find the best return on investment . The feasibility and sensitivity of the model are analyzed .

1. Preparation of the model

The time series ：

We usually use the method of time series to solve this kind of problem , There are several common methods of time series ：ARIMA Model 、ARCH/GARCH Model . because ARIMA It's a way to model data linearly and keep the prediction unchanged , Because the model can't reflect recent changes or merge new information . let me put it another way , It provides the best linear prediction for the sequence , So it has little effect in nonlinear model prediction . To model fluctuations , Need to use ARCH/GARCH Method . Here we use GARCH In this paper, the author analyzes it by using the following methods .

First , Check that the residual plot shows any volatility . Next , Square of observed residuals . If there is volatility , You should use ARCH/GARCH Modeling the volatility of a series , To reflect the

 

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