Before revision:   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.
After revision:  We assume that the agent has constant absolute risk aversion and aims at maximising the expected utility of the cash position at the end of time. The agent is then faced with the problem of balancing the market risk and the cost of a rapid execution. In particular we are interested in how the agent should go about optimally submitting orders. 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.