This thesis proposes a mathematical framework for studying feedback effects and endogenous risk in financial markets. We propose a multi-period model of a financial market with multiple assets, which takes into account the price impact generated by large shifts in supply and demand from financial institutions. Chapter 1 reviews the existing empirical and theoretical literature on feedback effects and motivates this thesis. Chapter 2 studies feedback effects from distressed selling in a large fund, in the case of a linear price impact model, while Chapter 3 extends such results to feedback effects from fire sales in multiple funds and allows for a general price impact function. Chapter 4 studies the impact of a large institutional investor keeping a fixed allocation/portion invested in each asset. We quantify the excess supply and demand generated in each case. The multi-period price dynamics in the presence of feedback effects is modeled as a Markov chain and we exhibit conditions under which it converges weakly, as the time step of the discrete-time model goes to zero, to the solution of a stochastic differential equation, for which we give the multi-dimensional drift and volatility explicitly. The study of the quadratic covariation process of the diffusion limit allows us to quantify the impact of feedback effects on the dependence structure of asset returns and the endogenous risk generated: under our model assumptions, we show that we can compute the impact of feedback effects on fund volatility and the spillover effects to other funds investing in the same assets. Finally, we give conditions for the identifiability of model parameters from time series of asset prices and build an estimator for the fund flows generated by systematic supply and demand by large financial institutions. We show that such estimator is consistent and derive a central limit theorem in Chapter 3. We illustrate our estimation procedure with two empirical examples.
