Erhan Bayraktar

Liquidation in Limit Order Books with Controlled Intensity

We consider a framework for solving optimal liquidation problems in limit order books. In particular, order arrivals are modeled as a point process whose intensity depends on the liquidation price. We set up a stochastic control problem in which the goal is to maximize the expected revenue from liquidating the entire position held. We solve this optimal liquidation problem for power-law and exponential-decay order book models and discuss several extensions. We also consider the continuous selling (or fluid) limit when the trading units are ever smaller and the intensity is ever larger. This limit provides an analytical approximation to the value function and the optimal solution. Using techniques from viscosity solutions we show that the discrete state problem and its optimal solution converge to the corresponding quantities in the continuous selling limit uniformly on compacts.

Estimating the Fractal Dimension of the S&P 500 Index Using Wavelet Analysis

S&P 500 index data sampled at one-minute intervals over the course of 11.5 years (January 1989- May 2000) is analyzed, and in particular the Hurst parameter over segments of stationarity (the time period over which the Hurst parameter is almost constant) is estimated. An asymptotically unbiased and efficient estimator using the log-scale spectrum is employed. The estimator is asymptotically Gaussian and the variance of the estimate that is obtained from a data segment of

OPTIMAL TRADE EXECUTION IN ILLIQUID MARKETS

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Stochastic Perron's method and verification without smoothness using viscosity comparison: The linear case

points is of order

Optimizing venture capital investments in a jump diffusion model

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Adaptive Poisson disorder problem

. Wavelet analysis is tailor made for the high frequency data set, since it has low computational complexity due to the pyramidal algorithm for computing the detail coefficients. This estimator is robust to additive non-stationarities, and here it is shown to exhibit some degree of robustness to multiplicative non-stationarities, such as seasonalities and volatility persistence, as well. This analysis shows that the market became more efficient in the period 1997-2000.

On the One-Dimensional Optimal Switching Problem

We study optimal trade execution strategies in financial markets with discrete order flow. The agent has a finite liquidation horizon and must minimize price impact given a random number of incoming trade counterparties. Assuming that the order flow

A Limit Theorem for Financial Markets with Inert Investors

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Pricing Asian Options for Jump Diffusion

is given by a Poisson process, we give a full analysis of the properties and computation of the optimal dynamic execution strategy. Extensions, whereby (a)

On the Multi-Dimensional Controller-and-Stopper Games

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