Mean–variance optimal trading problem subject to stochastic dominance constraints with second order autoregressive price dynamics

The efficient modeling of execution price path of an asset to be traded is an important aspect of the optimal trading problem. In this paper an execution price path based on the second order autoregressive process is proposed. The proposed price path is a generalization of the existing first order a...

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Vydané v:Mathematical methods of operations research (Heidelberg, Germany) Ročník 86; číslo 1; s. 29 - 69
Hlavní autori: Singh, Arti, Selvamuthu, Dharmaraja
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2017
Springer Nature B.V
Predmet:
Autoregressive processes
Business and Management
Calculus of Variations and Optimal Control; Optimization
Computer simulation
Cost engineering
Dynamic programming
Economic models
Exact solutions
Marketing
Markets
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Mutual funds
Operations research
Operations Research/Decision Theory
Original Article
Quadratic programming
Randomness
Risk
Stochastic models
Variance
Optimal trading
Stochastic dominance
Autoregressive behavior
Quadratic programming problem
Risk averse
Execution cost
ISSN:1432-2994, 1432-5217
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Shrnutí:The efficient modeling of execution price path of an asset to be traded is an important aspect of the optimal trading problem. In this paper an execution price path based on the second order autoregressive process is proposed. The proposed price path is a generalization of the existing first order autoregressive price path in literature. Using dynamic programming method the analytical closed form solution of unconstrained optimal trading problem under the second order autoregressive process is derived. However in order to incorporate non-negativity constraints in the problem formulation, the optimal static trading problems under second order autoregressive price process are formulated. For a risk neutral investor, the optimal static trading problem of minimizing expected execution cost subject to non-negativity constraints is formulated as a quadratic programming problem. Whereas, for a risk averse investor the variance of execution cost is considered as a measure for the timing risk, and the mean–variance problem is formulated. Moreover, the optimal static trading problem subject to stochastic dominance constraints with mean–variance static trading strategy as the reference strategy is studied. Using Static approximation method the algorithm to solve proposed optimal static trading problems is presented. With numerical illustrations conducted on simulated data and the real market data, the significance of second order autoregressive price path, and the optimal static trading problems is presented.
Bibliografia:ObjectType-Article-1
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ISSN:1432-2994
1432-5217
DOI:10.1007/s00186-017-0582-4