Levy过程驱动下单边限价订单簿中风险厌恶投资者的最优变现
Optimal liquidation for a risk averse investor in a one-sided limit order book driven by a Levy process
摘要：
在单边限价订单簿中，满足一些现实的假设，其中未受影响的价格过程遵循Levy过程，我们考虑一个市场代理，希望清算大量的股票。我们假设代理人具有恒定的绝对风险厌恶，目标是最大化现金头寸在时间结束时的期望效用。然后，代理人面临着平衡市场风险和快速执行成本的问题。我们特别感兴趣的是代理商如何以最佳方式提交订单。由于清算通常发生在很短的时间内，将风险建模为Levy过程应提供一个与观察到的市场数据具有良好统计拟合的现实模型，因此该模型应真实反映代理人的市场风险。我们减少优化问题的确定性的二维奇异问题，我们能够得到一个明确的解决方案的模型数据。特别是，我们找到了一个表达式的最佳干预边界，它完全覆盖的最优清算策略。
英文摘要：
In a one-sided limit order book, satisfying some realistic assumptions, where the unaffected price process follows a Levy process, we consider a market agent that wants to liquidate a large position of shares. 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, and thus the model should provide a realistic reflection of the agent's market risk. We 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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