PORTFOLIO LIQUIDATION IN DARK POOLS IN CONTINUOUS TIME

By Peter Kratz, Torsten Schoeneborn. 2012

62 citations recorded by the source corpus.

We consider an illiquid financial market where a risk averse investor has to liquidate a portfolio within a finite time horizon [0, T] and can trade continuously at a traditional exchange (the “primary venue”) and in a dark pool. At the primary venue, trading yields a linear price impact. In the dark pool, no price impact costs arise but order execution is uncertain, modeled by a multidimensional Poisson process. We characterize the costs of trading by a linear‐quadratic functional which incorporates both the price impact costs of trading at the primary exchange and the market risk of the position. The solution of the cost minimization problem is characterized by a matrix differential equation with singular boundary condition; by means of stochastic control theory, we provide a verification argument. If a single‐asset position is to be liquidated, the investor slowly trades out of her position at the primary venue, with the remainder being placed in the dark pool at any point in time. For multi‐asset liquidations this is generally not the case; for example, it can be optimal to oversize orders in the dark pool in order to turn a poorly balanced portfolio into a portfolio bearing less risk.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/d065a39f0dc0b231e33e8f609be8f951497bd978

Citations in the corpus

• Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting (2015, unknown): “In recent years models of optimal portfolio liquidation have been widely developed, see, e.g. [1], [2], [8], [10], [15], or [22], among many others.”