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Optimal investing stopping in stochastic environment

Optimal investing stopping in stochastic environment Purpose – The purpose of this paper is to investigate how to determine optimal investing stopping time in a stochastic environment, such as with stochastic returns, stochastic interest rate and stochastic expected growth rate. Design/methodology/approach – Transformation method was used for solving optimal stopping problem by providing a way to transform path‐dependent problem into a path‐independent one. Based on option pricing theory, optimal investing stopping time was thought of as an optimal executed timing problem of American‐style option. Findings – First, the authors transform a path‐dependent stop timing problem to a path‐independent one with transformation under very general conditions, to directly use the existing conclusion of optimal stopping time literature. Second, when dynamics of capital growth is homogeneous, the authors changed the two dimensional optimal stop timing problem into a single dimension problem based on the assumption of zero exercise costs. Third, the authors investigated the comparative dynamics about asset selling boundary on asset value, state variable and return predictability. With constant discount rate and growth rate, the optimal selling timing depends on the simple comparison between capital cost and growth rate. Originality/value – The paper's contributions to analysis method may be as follows. The authors demonstrate how to transform a path‐dependent stopping problem into a path‐independent one under general conditions. The transform method in this article can be applied to other path‐dependent optimal stopping problems. In particular, a Riccati ordinary differential equation for the transformation is set up. In most examples commonly met in finance, the equation can be solved explicitly. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png China Finance Review International Emerald Publishing

Optimal investing stopping in stochastic environment

Shuang Xu; Ran Zhang
China Finance Review International , Volume 3 (2): 22 – May 10, 2013
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Publisher
Emerald Publishing
Copyright
Copyright © 2013 Emerald Group Publishing Limited. All rights reserved.
ISSN
2044-1398
DOI
10.1108/20441391311330591
Publisher site
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Abstract

Purpose – The purpose of this paper is to investigate how to determine optimal investing stopping time in a stochastic environment, such as with stochastic returns, stochastic interest rate and stochastic expected growth rate. Design/methodology/approach – Transformation method was used for solving optimal stopping problem by providing a way to transform path‐dependent problem into a path‐independent one. Based on option pricing theory, optimal investing stopping time was thought of as an optimal executed timing problem of American‐style option. Findings – First, the authors transform a path‐dependent stop timing problem to a path‐independent one with transformation under very general conditions, to directly use the existing conclusion of optimal stopping time literature. Second, when dynamics of capital growth is homogeneous, the authors changed the two dimensional optimal stop timing problem into a single dimension problem based on the assumption of zero exercise costs. Third, the authors investigated the comparative dynamics about asset selling boundary on asset value, state variable and return predictability. With constant discount rate and growth rate, the optimal selling timing depends on the simple comparison between capital cost and growth rate. Originality/value – The paper's contributions to analysis method may be as follows. The authors demonstrate how to transform a path‐dependent stopping problem into a path‐independent one under general conditions. The transform method in this article can be applied to other path‐dependent optimal stopping problems. In particular, a Riccati ordinary differential equation for the transformation is set up. In most examples commonly met in finance, the equation can be solved explicitly.

Journal

China Finance Review International – Emerald Publishing

Published: May 10, 2013

Keywords: Stochastic processes; Investments; Stocks; Optimal investing stopping; Stock selling rule; Stochastic interest rate; Stochastic growth rate

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