2014/06/23 by Sakda Chaiworawitkul, Chaiworawitkul, Sakda, Patrick S. Hagan +3
Economics, Econometrics and Finance · Engineering · #49L20 #93E20 #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Reservoir Engineering and Simulation Methods #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1406.6090
openalex publication_date 2014/06/23 · openalex created_date 2022/08/19 · openalex updated_date 2026/07/28
This is the first in a series of papers in which we study an efficient\napproximation scheme for solving the Hamilton-Jacobi-Bellman equation for\nmulti-dimensional problems in stochastic control theory. The method is a\ncombination of a WKB style asymptotic expansion of the value function, which\nreduces the second order HJB partial differential equation to a hierarchy of\nfirst order PDEs, followed by a numerical algorithm to solve the first few of\nthe resulting first order PDEs. This method is applicable to stochastic systems\nwith a relatively large number of degrees of freedom, and does not seem to\nsuffer from the curse of dimensionality. Computer code implementation of the\nmethod using modest computational resources runs essentially in real time. We\napply the method to solve a general portfolio construction problem.\n