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
SN - 0927-7099
VL - 54
SP - 1179
EP - 1211
JO - Computational Economics
JF - Computational Economics
IS - 3
ER -