Optimal execution with dynamic risk adjustment

This paper considers the problem of optimal liquidation of a position in a risky security in a financial market, where price evolution are risky and trades have an impact on price as well as uncertainty in the filling orders. The problem is formulated as a continuous time stochastic optimal control...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2019-07
Main Authors: Cheng, Xue, Marina Di Giacinto, Tai-Ho, Wang
Format: Article
Language:English
Subjects:
Differential equations
Economic models
Optimal control
Optimization
Policies
Risk
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper considers the problem of optimal liquidation of a position in a risky security in a financial market, where price evolution are risky and trades have an impact on price as well as uncertainty in the filling orders. The problem is formulated as a continuous time stochastic optimal control problem aiming at maximizing a generalized risk-adjusted profit and loss function. The expression of the risk adjustment is derived from the general theory of dynamic risk measures and is selected in the class of \(g\)-conditional risk measures. The resulting theoretical framework is nonclassical since the target function depends on backward components. We show that, under a quadratic specification of the driver of a backward stochastic differential equation, it is possible to find a closed form solution and an explicit expression of the optimal liquidation policies. In this way it is immediate to quantify the impact of risk-adjustment on the profit and loss and on the expression of the optimal liquidation policies.
ISSN:2331-8422