In a general one-sided limit order book where the unaffected price process follows a Levy process, we consider the problem for an investor with constant absolute risk aversion to optimally liquidate a given large position of shares. Since liquidation normally takes place within a short period of time, modelling the risk as a Levy process should provide a realistic model with good statistical fit to observed market data, thus providing a realistic reflection of the investors market risk. We can reduce the optimisation problem to a deterministic two-dimensional singular problem, to which we are able to derive an explicit solution in terms of the model data. In particular we find an expression for the optimal intervention boundary, which completely characterise the optimal liquidation strategy.
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