# Optimal position targeting with stochastic linear-quadratic costs

Stefan Ankirchner; Thomas Kruse

Banach Center Publications (2015)

- Volume: 104, Issue: 1, page 9-24
- ISSN: 0137-6934

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topStefan Ankirchner, and Thomas Kruse. "Optimal position targeting with stochastic linear-quadratic costs." Banach Center Publications 104.1 (2015): 9-24. <http://eudml.org/doc/282247>.

@article{StefanAnkirchner2015,

abstract = {We consider the dynamic control problem of attaining a target position at a finite time T, while minimizing a linear-quadratic cost functional depending on the position and speed. We assume that the coefficients of the linear-quadratic cost functional are stochastic processes adapted to a Brownian filtration. We provide a probabilistic solution in terms of two coupled backward stochastic differential equations possessing a singularity at the terminal time T. We verify optimality of the candidate control by using a penalization argument. Special cases for which the problem has explicit solutions are discussed. Finally we illustrate our results in financial applications, where we derive optimal trading strategies for closing financial asset positions in markets with stochastic price impact and non-zero returns.},

author = {Stefan Ankirchner, Thomas Kruse},

journal = {Banach Center Publications},

keywords = {dynamic control problem; optimal position targeting; linear-quadratic cost functional; backward stochastic differential equations; financial mathematics},

language = {eng},

number = {1},

pages = {9-24},

title = {Optimal position targeting with stochastic linear-quadratic costs},

url = {http://eudml.org/doc/282247},

volume = {104},

year = {2015},

}

TY - JOUR

AU - Stefan Ankirchner

AU - Thomas Kruse

TI - Optimal position targeting with stochastic linear-quadratic costs

JO - Banach Center Publications

PY - 2015

VL - 104

IS - 1

SP - 9

EP - 24

AB - We consider the dynamic control problem of attaining a target position at a finite time T, while minimizing a linear-quadratic cost functional depending on the position and speed. We assume that the coefficients of the linear-quadratic cost functional are stochastic processes adapted to a Brownian filtration. We provide a probabilistic solution in terms of two coupled backward stochastic differential equations possessing a singularity at the terminal time T. We verify optimality of the candidate control by using a penalization argument. Special cases for which the problem has explicit solutions are discussed. Finally we illustrate our results in financial applications, where we derive optimal trading strategies for closing financial asset positions in markets with stochastic price impact and non-zero returns.

LA - eng

KW - dynamic control problem; optimal position targeting; linear-quadratic cost functional; backward stochastic differential equations; financial mathematics

UR - http://eudml.org/doc/282247

ER -

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