This article reviews the theory of imperfectly competitive financial markets, with special attention to recent contributions and rapidly growing areas of research. We highlight the methodological advances that have led to a unified analytic framework for static, dynamic, centralized, and decentralized markets. Accounting for imperfect competition has not only reshaped our understanding of financial market data but also underscored the importance of market structure, motivated novel policy tools and objectives, and opened new avenues for market design. We identify areas where new models and techniques could enable further progress on equilibrium and market design analyses for markets with large players.

Decentralized trading motivates financial innovation, making synthetic products like derivatives nonredundant, even when all traders trade all assets. This nonredundancy arises because derivatives affect cross-security inference (information) and, in markets with large traders, equilibrium price impact (liquidity). The efficient securities differ from the underlying assets. While the market index/mutual funds are efficient in decentralized markets with competitive investors, heterogeneous portfolios that balance index tracking with liquidity transformation become efficient in markets with large traders. Efficient securities facilitate the trading of all fundamental risks but generally forgo hedging all contingencies to minimize the price impact costs associated with risk sharing and diversification.