2013/04/10 by Damiano Brigo, Brigo, Damiano, Di Graziano, Giuseppe +1
Economics, Econometrics and Finance · #60H10 #60J60 #91B70 #FOS: Economics and business #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #Monetary Policy and Economic Impact #Risk Management (q-fin.RM) #Statistical Finance (q-fin.ST) #Stochastic processes and financial applications #Trading and Market Microstructure (q-fin.TR) #msc:60H10 #msc:60J60 #msc:91B70 #q-fin.RM #q-fin.ST #q-fin.TR
paper · pdf · doi:10.48550/arxiv.1304.2942
openalex publication_date 2013/04/10 · arxiv created 2014/05/09 · arxiv updated 2014/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We solve a version of the optimal trade execution problem when the mid asset price follows a displaced diffusion. Optimal strategies in the adapted class under various risk criteria, namely value-at-risk, expected shortfall and a new criterion called "squared asset expectation" (SAE), related to a version of the cost variance measure, are derived and compared. It is well known that displaced diffusions (DD) exhibit dynamics which are in-between arithmetic Brownian motions (ABM) and geometric Brownian motions (GBM) depending of the choice of the shift parameter. Furthermore, DD allows for changes in the support of the mid asset price distribution, allowing one to include a minimum permitted value for the mid price, either positive or negative. We study the dependence of the optimal solution on the choice of the risk aversion criterion. Optimal solutions across criteria and asset dynamics are comparable although differences are not negligible for high levels of risk aversion and low market impact assets. This is illustrated with numerical examples.