On Optimal Risk Sensitive Execution Problem

In the execution of large institutional transactions, a trading strategy must be de-termined that balances the risk of delayed execution against the cost of rapid execution.In this thesis, we deal with optimal risk sensitive execution for trading of fnancial se-curities. It is divided into three parts to study both a single-asset and portfolio case toderive both dynamic and static optimal trading strategies with the aim of minimizing acombination of volatility risk and transaction costs.In the frst part, we derive dynamic optimal execution strategies that minimizethe exponential decay function of income from liquidating a large block of equity overa fxed time horizon, the decay constant is a measure of risk-aversion. Specifcally,given a price-impact function that yields the execution price of an individual trade asa function of the number of shares traded and serially-correlated state variables whichrepresents disclosed information about the security, we obtain the optimal sequenceof trades as a function of state variables-closed-form expressions in some cases-thatminimizes the exponential decay function of income of liquidating a large block of Sshares within T periods.Then we move on to extend our analysis to the portfolio case in the second partin which cross price efects of securities can have an important ramifcation on theexecution cost. To more precisely model the price impact, we divide impact into apermanent and a temporary component.Finally, ouranalysisfallsintothestaticcategory. Weareconcernedwith theliqui-dation of a single asset with the aim of minimizing a combination of volatility risk andexecution costs arising from permanent and temporary market impact. For a simplelinear cost model, we explicitly construct the efcient frontier, which have minimumexpected cost for a given level of risk.Wealsoconductsimulatedanalysesintheprogressionofourmodels’construction against classic ones by Bertsimas and Almgren. Compared to Bertsimas’s model,ours exhibits better control of risk and execution costs. When it comes to Almgren’s,our model shows more robustness.