Abstract:

Since the outbreak of COVID-19， financial markets worldwide have experienced frequent significant fluctuations， occasionally triggering circuit breaker mechanisms， leading to numerous instances of stocks plummeting. The vast changes in market volatility and its uncertain distribution have made it challenging for investors to accurately predict market dynamics， a phenomenon referred to as ambiguous volatility. Consequently， how ambiguous volatility affects market liquidity is asked. How does it impact investors' trading intensity， expected wealth， and trading volume？ These questions are not only important but also intriguing for policymakers and investors alike. In light of this， a continuous-time market microstructure model incorporating ambiguous volatility within a strategic trading framework is constructed and stochastic optimal control theory is applied to solve the corresponding Hamilton-Jacobi-Bellman-Isaacs （HJBI） equation， thereby explicitly revealing the impact of ambiguous volatility on informed traders' trading strategies and market quality. The findings indicate that an increase in ambiguous volatility leads to a decrease in the optimal trading intensity of informed traders， worsened market liquidity， a reduction in the expected total trading volume of risky assets， and a decrease in informed traders' expected wealth and overall profits. These effects contrast sharply with those observed under constant volatility. It not only deepens our existing understanding of the differences between ambiguous and constant volatility but also provides theoretical guidance for designing market mechanisms under conditions of uncertain volatility in this paper. It emphasizes the importance of reducing market ambiguity to maintain normal and healthy market operations and to prevent systemic financial risks， highlighting the need for further empirical research to accurately measure ambiguous volatility.

Key words: continuous time market microstructure, ambiguous volatility, trading strategy, market quality