A procedure is developed for the valuation of options when there are two underlying state variables. The approach involves an extension of the lattice binomial approach developed by Cox, Ross, and Rubinstein to value options on a single asset. Details are given on how the jump probabilities and jump amplitudes may be obtained when there are two state variables. This procedure can be used to pri...

I this paper, we investigate the methodological issue of determining the number of state variables required for options pricing. After showing the inadequacy of the principal component analysis approach, which is commonly used in the literature, we adopt a nonparametric regression technique with nonlinear principal components extracted from the implied volatilities of various moneyness and matu...

Efficient representations and solutions for large decision problems with continuous and discrete variables are among the most important challenges faced by the designers of automated decision support systems. In this paper, we describe a novel hybrid factored Markov decision process (MDP) model that allows for a compact representation of these problems, and a new hybrid approximate linear progr...

Dynamic textures are image sequences which contain moving scenes such as a flowing river, drifting smoke, waving foliage, etc. Such image sequences have dynamical properties that are related to motion in the physical world. In this paper, we propose a novel analytical tool for analyzing dynamic textures. The key idea is to exploit the properties of the impulse responses of the state variables c...

The parameter domain for which the quasi-steady state assumption is valid can be considerably extended merely by a simple change of variable. This is demonstrated for a variety of biologically significant examples taken from enzyme kinetics, immunology and ecology.

A new set of averaging rules is put forward that exactly determines the means of air temperature, mixing ratio, and velocity by incorporating weighting factors in accordance with physical conservation laws. For the temperature and velocity, respectively, the means calculated according to these rules are shown to be in accordance with the gas law and the most fundamental definition from classica...

This article investigates the pricing of options when a need arises to carry a path dependent auxiliary state variable. Examples of such problems include the pricing of interest rate claims in a Heath Jarrow Morton paradigm, where the underlying forward rates follow a Markovian process, and the pricing of equity options, when the underlying asset price follows a GARCH process. In the former cas...

Macroscopic quantities beyond effective elastic tensors are presented that can be used to assess the local state of stress within a composite in the linear elastic regime. These are presented in a general homogenization context. It is shown that the gradient of the effective elastic property can be used to develop a lower bound on the maximum pointwise equivalent stress in the fine-scale limit....

The paper studies the ability possessed by recurrent neural networks to model dynamic systems when some relevant state variables are not measurable. Neural architectures based on virtual states—which naturally arise from a space state representation—are introduced and compared with the more traditional neural output error ones. Despite the evident potential model ability possessed by virtual st...

Best Choice of State Variables for Tracking Coordinated Turns Fredrik Gustafsson Alf J. Isaksson Abstract A standard approach to tracking is to use the Extended Kalman Filter (EKF) applied to a non-linear state-space model. The main contribution here is a general analysis of the linearization error made in the EKF, and the result is applied to a particular tracking problem. In target tracking o...