On the Numerical Solution of Mertonian Control Problems: A Survey of the Markov Chain Approximation Method for the Working Economist

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

On the Numerical Solution of Mertonian Control Problems : A Survey of the Markov Chain Approximation Method for the Working Economist. / Ellersgaard, Simon.

In: Computational Economics, Vol. 54, No. 3, 2019, p. 1179-1211.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Ellersgaard, S 2019, 'On the Numerical Solution of Mertonian Control Problems: A Survey of the Markov Chain Approximation Method for the Working Economist', Computational Economics, vol. 54, no. 3, pp. 1179-1211. https://doi.org/10.1007/s10614-018-9865-y

APA

Ellersgaard, S. (2019). On the Numerical Solution of Mertonian Control Problems: A Survey of the Markov Chain Approximation Method for the Working Economist. Computational Economics, 54(3), 1179-1211. https://doi.org/10.1007/s10614-018-9865-y

Vancouver

Ellersgaard S. On the Numerical Solution of Mertonian Control Problems: A Survey of the Markov Chain Approximation Method for the Working Economist. Computational Economics. 2019;54(3):1179-1211. https://doi.org/10.1007/s10614-018-9865-y

Author

Ellersgaard, Simon. / On the Numerical Solution of Mertonian Control Problems : A Survey of the Markov Chain Approximation Method for the Working Economist. In: Computational Economics. 2019 ; Vol. 54, No. 3. pp. 1179-1211.

Bibtex

@article{22c6c257838b4885b573016544866505,
title = "On the Numerical Solution of Mertonian Control Problems: A Survey of the Markov Chain Approximation Method for the Working Economist",
abstract = "Analytic solutions to HJB equation in mathematical finance are relatively hard to come by, which stresses the need for numerical procedures. In this paper we provide a self-contained exposition of the finite-horizon Markov chain approximation method as championed by Kushner and Dupuis. Furthermore, we provide full details as to how well the algorithm fares when we deploy it in the context of Merton type optimisation problems. Assorted issues relating to implementation and numerical accuracy are thoroughly reviewed, including multidimensionality and the positive probability requirement, the question of boundary conditions, and the choice of parametric values.",
keywords = "Finite difference approximation, HJB equation, Merton problem",
author = "Simon Ellersgaard",
year = "2019",
doi = "10.1007/s10614-018-9865-y",
language = "English",
volume = "54",
pages = "1179--1211",
journal = "Computational Economics",
issn = "0927-7099",
publisher = "Springer",
number = "3",

}

RIS

TY - JOUR

T1 - On the Numerical Solution of Mertonian Control Problems

T2 - A Survey of the Markov Chain Approximation Method for the Working Economist

AU - Ellersgaard, Simon

PY - 2019

Y1 - 2019

N2 - Analytic solutions to HJB equation in mathematical finance are relatively hard to come by, which stresses the need for numerical procedures. In this paper we provide a self-contained exposition of the finite-horizon Markov chain approximation method as championed by Kushner and Dupuis. Furthermore, we provide full details as to how well the algorithm fares when we deploy it in the context of Merton type optimisation problems. Assorted issues relating to implementation and numerical accuracy are thoroughly reviewed, including multidimensionality and the positive probability requirement, the question of boundary conditions, and the choice of parametric values.

AB - Analytic solutions to HJB equation in mathematical finance are relatively hard to come by, which stresses the need for numerical procedures. In this paper we provide a self-contained exposition of the finite-horizon Markov chain approximation method as championed by Kushner and Dupuis. Furthermore, we provide full details as to how well the algorithm fares when we deploy it in the context of Merton type optimisation problems. Assorted issues relating to implementation and numerical accuracy are thoroughly reviewed, including multidimensionality and the positive probability requirement, the question of boundary conditions, and the choice of parametric values.

KW - Finite difference approximation

KW - HJB equation

KW - Merton problem

UR - http://www.scopus.com/inward/record.url?scp=85056404484&partnerID=8YFLogxK

U2 - 10.1007/s10614-018-9865-y

DO - 10.1007/s10614-018-9865-y

M3 - Journal article

AN - SCOPUS:85056404484

VL - 54

SP - 1179

EP - 1211

JO - Computational Economics

JF - Computational Economics

SN - 0927-7099

IS - 3

ER -

ID: 230392266