Parameter optimization for differential equations in asset price forecasting

Ahmet Duran*, Gunduz Caginalp

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

A system of nonlinear asset flow differential equations (AFDE) gives rise to an inverse problem involving optimization of parameters that characterize an investor population. The optimization procedure is used in conjunction with daily market prices (MPs) and net asset values to determine the parameters for which the AFDE yield the best fit for the previous n days. Using these optimal parameters, the equations are computed and solved to render a forecast for MPs for the following days. For a number of closed-end funds, the results are statistically closer to the ensuing MPs than the default prediction of random walk (RW). In particular, we perform this optimization by a nonlinear computational algorithm that combines a quasi-Newton weak line search with the Broyden-Fletcher-Goldfarb-Shanno formula. We develop a nonlinear least-square technique with an initial value problem (IVP) approach for arbitrary stream data by focusing on the MP variable P since any real data for the other three variables B, ζ1, and ζ2 in the dynamical system is not available explicitly. We minimize the sum of exponentially weighted squared differences F[K̃] between the true trading prices from Day i to Day i+n-1, and the corresponding computed MPs obtained from the first row vector of the numerical solution U of the IVP with AFDE for ith optimal parameter vector, where K̃ is an initial parameter vector. Here, the gradient (Δ F(x)) is approximated by using the central difference formula, and step length s is determined by the backtracking line search. One of the novel components of the proposed asset flow optimization forecast algorithm is a dynamic initial parameter pool that contains most recently used successful parameters, besides the various fixed parameters from a set of grid points in a hyper-box.

Original languageEnglish
Pages (from-to)551-574
Number of pages24
JournalOptimization Methods and Software
Volume23
Issue number4
DOIs
Publication statusPublished - Aug 2008
Externally publishedYes

Keywords

  • Asset flow differential equations
  • Data analysis in mathematical finance and economics
  • Financial market dynamics
  • Inverse problem of parameter estimation
  • Market return prediction algorithm
  • Numerical nonlinear optimization

Fingerprint

Dive into the research topics of 'Parameter optimization for differential equations in asset price forecasting'. Together they form a unique fingerprint.

Cite this