Abstract
In recent years, in pursuit of higher returns, people began to try the combination of bitcoin and gold. This study explored how to use the current and past prices of gold and bitcoin to get the best investment strategies for the next day to get the maximum return. Firstly, by preprocessing and analyzing the historical price data of gold and bitcoin in five years, the long- and short-term memory (LSTM) recurrent neural network was used to establish the price prediction models of gold and bitcoin. Secondly, the dynamic programming method was applied to transform the solution problem into the optimization problem, and the state equation of the optimal trading strategy was obtained through the determined objective function and constraint conditions. Thus, the total value of the original trading strategy determined using 1,000 $ in cash after five years of investment was calculated to be 62692.13 $. Then two methods were introduced to prove the rationality of the optimal trading strategy. Finally, the sensitivity of commission cost to trading strategies was deeply analyzed by changing the commission ratio of gold and bitcoin using the control variable method. The results show that the established price prediction models have good prediction accuracy and can accurately predict the future prices of gold and bitcoin assets. The trading strategy based on the price forecasting model and dynamic programming method can maximize the return on investment for investors. The research provides theoretical guidance for investors on choosing portfolios and trades to get the maximum return.
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