Dynamic portfolio choice with uncertain rare-events risk in stock and cryptocurrency markets

Abstract

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.

The implication of cryptocurrency volatility on five largest African financial system stability

“…The study concludes that no evidence suggests cryptocurrency is a strong or weak safe haven for the traditional market. In managing investment risk arising from market uncertainty, Lv et al (2023) found evidence to support the conclusion that price diffusion ambiguity is critical in influencing investor portfolio decisions, especially during rare events, in both markets.…”

Application of Portfolio Optimization to Achieve Persistent Time Series

“…Other authors proposed to tackle the problem on different grounds, for example by incorporating the occasional presence of rare events [11] or phrasing it as a sorting problem [4]. Some even tried incorporating volatility as an additional asset [10].…”