2012/04/12 by Christopher Lorenz, Lorenz, Christopher, Alexander Schied +1 · 1 citation
Economics, Econometrics and Finance · #49N10 #60H30 #91G80 #93E20 #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #Trading and Market Microstructure (q-fin.TR)
paper · pdf · doi:10.48550/arxiv.1204.2716
openalex publication_date 2012/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a complete solution to the problem of minimizing the expected\nliquidity costs in presence of a general drift when the underlying market\nimpact model has linear transient price impact with exponential resilience. It\nturns out that this problem is well-posed only if the drift is absolutely\ncontinuous. Optimal strategies often do not exist, and when they do, they\ndepend strongly on the derivative of the drift. Our approach uses elements from\nsingular stochastic control, even though the problem is essentially\nnon-Markovian due to the transience of price impact and the lack in Markovian\nstructure of the underlying price process. As a corollary, we give a complete\nsolution to the minimization of a certain cost-risk criterion in our setting.\n