In this article, we develop a general CARA framework to study optimal execution and to price block trades. We prove existence and regularity results for optimal liquidation strategies and we provide several differential characterizations. We also give two different proofs that the usual restriction to deterministic liquidation strategies is optimal. In addition, we focus on the important topic of block trade pricing and we therefore give a price to nancial (il)liquidity. In particular, we provide a closed-form formula for the price a block trade when there is no time constraint to liquidate, and a differential characterization in the time-constrained case. Numerical methods are eventually discussed.
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Optimal execution and block trade pricing.pdf