Аннотация:
A starting point for this work is the paper of Almgren and Chriss (1999), which is very popular among practitioners, where the problem of optimal portfolio liquidation is studied. In their setting a time-consistent liquidation strategy is obtained as a result of deterministic mean-variance optimization. There are several desired properties that are missing in their strategy. Strategies used in practice have a decreasing in the position size relative selling speed. It is further desirable that the strategy has its intrinsic time horizon (which is increasing in the number of stocks to liquidate). Also it is more interesting to optimize over all adapted trading strategies rather than over the deterministic ones.
Instead of performing mean-variance optimization over deterministic strategies, we optimize the value of a dynamic risk measure over all adapted ones. In such a setting dynamic programming principle does not typically hold. However, in our particular problem we find explicit formulas for the optimal strategy. This strategy is time-consistent and has the desired properties mentioned in the previous paragraph. This is a joint work with A. Selivanov.
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