On optimal risk sensitive execution problem

This paper considers the risk sensitive optimal execution problem. In the financial market, trading(buying or selling) of large amount of assets usually causes moving of the price to unfavorable direction and further generates additional trading cost. The optimal execution problem is seeking the best execution strategy(control) in a given horizon to trade(buy or sell) certain amount of asset in order to maximize the profit. In this work, instead of considering the sole objective of maximizing the expected profit, we consider the risk sensitive formulation of such a problem, in which the execution risk is combined implicitly. By using the stochastic control approach, the analytical optimal execution strategy is derived. Using different risk sensitive parameter, our model could generate different mean-variance efficient execution strategy, which provides the investor freedom to adjust the execution strategy. Comparing with the traditional risk neutral formulation, our model shows prominent feature in controlling the execution risk.