A Numerical Method for Solving Stochastic Optimal Control Problems with Linear Control

Chavanasporn, Walailuck; Ewald, Christian‐Oliver

doi:10.2139/ssrn.1645006

Cited by 3 publications

(3 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to find V a (x), which comprises the two parts V a0 (x) for x < x * a and V ak (x) for x > x * a , we apply the numerical method for solving stochastic optimal control problem with linear control developed in Chavanasporn and Ewald (2010). Following this approach, we interpolate the value function on a discrete grid by quadratic spline functions (Fig.…”

Section: Investment Modelmentioning

confidence: 99%

See 1 more Smart Citation

Privatization of businesses and flexible investment: a real option approach

Chavanasporn

Ewald

2011

Decisions Econ Finan

Self Cite

View full text Add to dashboard Cite

In this article, we study the situation, where the opportunity is given to invest into a government-owned business by partial privatization to a private company. After payment of an initial installment cost, the private company's investments are flexible within a range [0, k] until the business is completed. We model the problem in a real option framework, using geometric mean reversion to describe the dynamics of the business. We determine the optimal time for the private company to enter and pay the initial installment cost as well as the optimal dynamic investment strategy that it follows afterward. For the latter, analytic solution cannot be obtained. We use quadratic splines in order to solve the corresponding dynamic programming problem. Finally, we determine the optimal degree of privatization in our model from the government's perspective.

show abstract

Section: Investment Modelmentioning

confidence: 99%

“…Due to the complexity of the modeling framework, we will not be able to solve this part analytically. Instead, we apply the numerical method developed by Chavanasporn and Ewald (2010) for solving stochastic optimal control problems with linear control, using quadratic splines to approximate the value function.…”

Section: Introductionmentioning

confidence: 99%

Privatization of businesses and flexible investment: a real option approach

Chavanasporn

Ewald

2011

Decisions Econ Finan

Self Cite

View full text Add to dashboard Cite

show abstract

“…In , the authors examined an alternative method of deriving numerical solutions to continuous‐time finite‐horizon SOC problems. The authors in introduced a numerical method to solve SOC problems, which are linear in the control. In , the authors investigated stochastic optimal strategy for unknown linear discrete‐time system quadratic zero‐sum games in input‐output form with communication imperfections.…”

Section: Introductionmentioning

confidence: 99%

A Computational Method for Stochastic Optimal Control Problems in Financial Mathematics

Kafash

Delavarkhalafi

Karbassi

2015

Asian Journal of Control

View full text Add to dashboard Cite

Principle of optimality or dynamic programming leads to derivation of a partial differential equation (PDE) for solving optimal control problems, namely the Hamilton‐Jacobi‐Bellman (HJB) equation. In general, this equation cannot be solved analytically; thus many computing strategies have been developed for optimal control problems. Many problems in financial mathematics involve the solution of stochastic optimal control (SOC) problems. In this work, the variational iteration method (VIM) is applied for solving SOC problems. In fact, solutions for the value function and the corresponding optimal strategies are obtained numerically. We solve a stochastic linear regulator problem to investigate the applicability and simplicity of the presented method and prove its convergence. In particular, for Merton's portfolio selection model as a problem of portfolio optimization, the proposed numerical method is applied for the first time and its usefulness is demonstrated. For the nonlinear case, we investigate its convergence using Banach's fixed point theorem. The numerical results confirm the simplicity and efficiency of our method.

show abstract

Privatization of Businesses and Flexible Investment: A Real Option Approach

Chavanasporn

Ewald

2010

SSRN Journal

View full text Add to dashboard Cite

A Numerical Method for Solving Stochastic Optimal Control Problems with Linear Control

Cited by 3 publications

References 12 publications

Privatization of businesses and flexible investment: a real option approach

Privatization of businesses and flexible investment: a real option approach

A Computational Method for Stochastic Optimal Control Problems in Financial Mathematics

Privatization of Businesses and Flexible Investment: A Real Option Approach

Contact Info

Product

Resources

About