Optimal liquidation under partial information with price impact

Autor: Zehra Eksi, Rüdiger Frey, Michaela Szölgyenyi, Katia Colaneri
Rok vydání: 2020
Předmět:
Statistics and Probability
Mathematical optimization
Comparison principle
Optimization problem
101024 Wahrscheinlichkeitstheorie
Stochastic filtering
Markov process
Optimal liquidation
01 natural sciences
Piecewise deterministic Markov Process
Viscosity solutions
FOS: Economics and business
010104 statistics & probability
symbols.namesake
Bellman equation
FOS: Mathematics
101024 Probability theory
0101 mathematics
Mathematics - Optimization and Control
Mathematics
Stochastic control
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Markov chain
Applied Mathematics
Probability (math.PR)
010102 general mathematics
Mathematical Finance (q-fin.MF)
101007 Financial mathematics
Settore MAT/06 - Probabilita' e Statistica Matematica
Quantitative Finance - Mathematical Finance
Optimization and Control (math.OC)
101007 Finanzmathematik
Modeling and Simulation
Piecewise
symbols
Viscosity solution
Jump process
Mathematics - Probability
Zdroj: Stochastic Processes and their Applications. 130:1913-1946
ISSN: 0304-4149
DOI: 10.1016/j.spa.2019.06.004
Popis: 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 finite-state 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.
Databáze: OpenAIRE
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