An application of interacting multiple model tracking method to financial modeling and asset allocation

This paper describes a continuous-time-state-process, discrete-time-observation, Interacting Multiple Model (IMM) tracking algorithm, and its applications to financial market modeling and asset allocation. A system state is modeled as a continuous-time, affine-Gaussian stochastic dynamical process driven by a white process noise, as well as structural changes modeled by a finite-state, continuous-time, Markov process. The system generally assumes multiple models with different state space dimensions and an affine-Gaussian state jump whenever a model transition occurs. The underlying problem is a standard filtering problem for estimating the system state based on a sequence of discrete-time, linear-Gaussian observations of partial system states. As our first attempt for applying the IMM methods to financial market modeling, we will use a rather naïve switching process using simple multiple linear stochastic system models.