Projects per year
Abstract
We study the optimal liquidation problem in a market model where the bid price follows a geometric pure jump process whose local characteristics are driven by an unobservable finitestate Markov chain and by the liquidation rate. This model is consistent with stylized facts of high frequency data such as the discrete nature of tick data and the clustering in the order flow. We include both temporary and permanent effects into our analysis. We use stochastic filtering to reduce the optimal liquidation problem to an equivalent optimization problem under complete information. This leads to a stochastic control problem for piecewise deterministic Markov processes (PDMPs). We carry out a detailed mathematical analysis of this problem. In particular, we derive the optimality equation for the value function, we characterize the value function as continuous viscosity solution of the associated dynamic programming equation, and we prove a novel comparison result. The paper concludes with numerical results illustrating the impact of partial information and price impact on the value function and on the optimal liquidation rate.
Original language  English 

Pages (fromto)  1913  1946 
Journal  Stochastic Processes and their Applications 
Volume  130 
Issue number  4 
DOIs  
Publication status  Published  2020 
Austrian Classification of Fields of Science and Technology (ÖFOS)
 101024 Probability theory
 101007 Financial mathematics
Projects
 1 Finished

Stochastic Filtering and Corporate and Sovereign Credit Risk
Frey, R. (PI  Project head), Damian, C. (Researcher), Hirk, R. (Researcher), Hornik, K. (Researcher), Pichler, S. (Researcher) & Szölgyenyi, M. (Researcher)
1/04/15 → 31/03/20
Project: Research funding