**Keywords:**Liquidation Strategies, Monte-Carlo, Derivatives, Tikhonov regularization, Price Impact, Intra-day Price.

In this report, we analyze the liquidation process of a given portfolio in the context of static strategies. By a static strategy we mean, one that does not take into account the flow of information on price changes during the control process. It tries to perform in some optimal sense to minimize losses.

We seek for static strategies because those are typically the one used in situations of stress in the case of a fund collapse.

Thus, we want to study the risk associated to the portfolio under a liquidation process more than the optimal strategy itself.We observe that the classical models might lead to instabilities and display lack of robustness.

We propose an improvement of the variance model which tackles the effects of the intra-day changes and impact price.

We then present a model that reduces the conditional value at risk (CVaR) and the variance at the same time. We do this by performing a Cholesky decomposition of the covariance matrix and adding to it a Tikhonov regularization term. Although this report presents an optimal liquidation of portfolio point of view, we can apply the concepts presented herein to a problem of optimal allocation of portfolios.

The present study may be of interest to risk management of central counterparties and clearing houses. In particular, it could be used for the computation of margins associated to portfolios.

**MSC 2000:**91B30

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