Abstract
In order to form a reasonable investment strategy, we analyze the two currency assets, such as gold and Bitcoin, after collecting the price of gold and bitcoin in a five-year trading period from 9/11/2016 to 9/10/2021. We deliver a twostage model based on asset price prediction, which makes a portfolio decision each trading day to maximize profits as follows: (1) We establish a mathematical model that gives the best one-day trading strategy based solely on the price data as of that day. We deduce the model of the optimal investment strategy of a single asset under the condition that the future price trend is known and proves its optimality. (2) Using the mathematical model constructed, we calculate how much investment value will have by 9/10/2021 and prove that the given strategy is optimal, assuming that 9/11/2016 has 1000 dollars. (3) Finally, we conduct a sensitivity analysis of the established model and discuss how transaction costs affect strategies and outcomes. Considering the simplification of the model, we would further take more factors, such as the holiday effect of the investment market and the relevant regulations of different exchanges, into account in future work.
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