Lv Wujun, Pang Tao, Xia Xiaobao, Yan Jingzhou
Department of Statistics, College of Science, Donghua University, No. 2999 Renmin North Road, Songjiang District, Shanghai, 201620 China.
Department of Mathematics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27695-8205 USA.
Financ Innov. 2023;9(1):73. doi: 10.1186/s40854-023-00472-8. Epub 2023 Apr 5.
In response to the unprecedented uncertain rare events of the last decade, we derive an optimal portfolio choice problem in a semi-closed form by integrating price diffusion ambiguity, volatility diffusion ambiguity, and jump ambiguity occurring in the traditional stock market and the cryptocurrency market into a single framework. We reach the following conclusions in both markets: first, price diffusion and jump ambiguity mainly determine detection-error probability; second, optimal choice is more significantly affected by price diffusion ambiguity than by jump ambiguity, and trivially affected by volatility diffusion ambiguity. In addition, investors tend to be more aggressive in a stable market than in a volatile one. Next, given a larger volatility jump size, investors tend to increase their portfolio during downward price jumps and decrease it during upward price jumps. Finally, the welfare loss caused by price diffusion ambiguity is more pronounced than that caused by jump ambiguity in an incomplete market. These findings enrich the extant literature on effects of ambiguity on the traditional stock market and the evolving cryptocurrency market. The results have implications for both investors and regulators.
针对过去十年前所未有的不确定罕见事件，我们通过将传统股票市场和加密货币市场中出现的价格扩散模糊性、波动率扩散模糊性和跳跃模糊性整合到一个单一框架中，推导出一个半封闭形式的最优投资组合选择问题。我们在两个市场中得出以下结论：第一，价格扩散和跳跃模糊性主要决定检测误差概率；第二，最优选择受价格扩散模糊性的影响比受跳跃模糊性的影响更显著，而受波动率扩散模糊性的影响微不足道。此外，投资者在稳定市场中往往比在波动市场中更具进取性。其次，给定较大的波动率跳跃幅度，投资者倾向于在价格下跌跳跃期间增加其投资组合，而在价格上涨跳跃期间减少投资组合。最后，在不完全市场中，价格扩散模糊性造成的福利损失比跳跃模糊性造成的福利损失更为明显。这些发现丰富了关于模糊性对传统股票市场和不断发展的加密货币市场影响的现有文献。研究结果对投资者和监管机构都有启示意义。
