This talk explores evolutionary models of asset markets in mathematical finance, in which many interacting agents compete for capital. We focus on the asymptotic dynamics of such systems—particularly which strategies accumulate wealth faster than others. A key feature of our approach is the existence of strategies that outperform others irrespective of competing agents' behavior, influencing the market's long-term characteristics. Unlike traditional models, we examine endogenous price formation, offering a new perspective on market evolution. I will review foundational and recent results, highlighting insights into strategy dominance and market dynamics.