2025/03/07 by Ackermann, Julia, Kruse, Thomas, Urusov, Mikhail · 1 citation
#FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Probability (math.PR) #Trading and Market Microstructure (q-fin.TR)
paper · doi:10.48550/arxiv.2503.05594
We analyze a continuous-time optimal trade execution problem in multiple assets where the price impact and the resilience can be matrix-valued stochastic processes that incorporate cross-impact effects. In addition, we allow for stochastic terminal and running targets. Initially, we formulate the optimal trade execution task as a stochastic control problem with a finite-variation control process that acts as an integrator both in the state dynamics and in the cost functional. We then extend this problem continuously to a stochastic control problem with progressively measurable controls. By identifying this extended problem as equivalent to a certain linear-quadratic stochastic control problem, we can use established results in linear-quadratic stochastic control to solve the extended problem. This work generalizes [Ackermann, Kruse, Urusov; FinancStoch'24] from the single-asset setting to the multi-asset case. In particular, we reveal cross-hedging effects, showing that it can be optimal to trade in an asset despite having no initial position. Moreover, as a subsetting we discuss a multi-asset variant of the model in [Obizhaeva, Wang; JFinancMark'13].