Portfolio strategies for a large trader.

Summary Traditional models of market finance do not explicitly account for the volume traded, although the price always reflects an equality of supply and demand. The aim of this thesis is precisely to account quantitatively for the impact of an agent trading a large number of assets, highlighting its link to market paradoxes and anomalies, and to develop appropriate hedging and arbitrage strategies. In the options market, the supply-demand imbalance requires a synthetic hedging strategy, which causes feedback effects on the option price, illustrating the so-called portfolio insurance paradox. From a concise model giving rise to a realistic bid-ask spread and a volatility smile, we develop concrete strategies based on inventory costs and information asymmetries.