In recent years, high-frequency trading has shaped the dynamics of equity markets. Within this context, this thesis develops and evaluates two proprietary strategies applied to the constituents of the FTSE MIB index, the main benchmark of the Italian equity market. The first contribution is a market making strategy, where quoted prices incorporate a premium to account for expected market impact, while a hedging offset is introduced to control exposures to systematic factors. These factors are extracted through principal component analysis, after cleaning the empirical covariance matrix of returns with Random Matrix Theory to separate signal from noise. The discussion then turns to the closing auction, where another strategy is designed to exploit the unique opportunities specific to this phase. In particular, the strategy determines the optimal quantities to submit by solving a convex quadratic optimization problem that balances expected profitability with the variance of the residual portfolio, which is computed through interior point methods implemented via Newton iterations to achieve computational efficiency. Both strategies are tested in a proprietary event-driven backtester that reproduces order-by-order market microstructure, and the results show consistent profitability, robustness across stocks and conditions, and effective control of inventory imbalances. Future research may extend these methodologies to other indices and to strategies operating simultaneously across multiple benchmarks, thereby exploiting overlaps to offset risks more efficiently and to investigate cross-market dynamics.