This paper surveys the classification of integrable evolution equations whose field variables
take values in an associative algebra, which includes matrix, Clifford, and group algebra …

An Affine Term Structure Model (ATSM) is said to be solvable if the pricing problem has an
explicit solution, ie, the corresponding Riccati ordinary differential equations have a regular …

This paper extends to the multiasset framework the closed-form solution for options with
stochastic volatility derived in Heston (1993) and Ball and Roma (1994). This extension …

We derive some restrictions on the possible degrees of algebraic invariant curves and on
the possible form of algebraic integrating factors, for plane polynomial vector fields whose …

This research monograph provides an introduction to tractable multidimensional diffusion
models, where transition densities, Laplace transforms, Fourier transforms, fundamental …

An algebra of rank three is a commutative, finite dimensional algebra that may be defined by
the property that every element generates a subalgebra of dimension not greater than two …

A finite-dimensional real vector space V equipped with a bilinear product xy is said to be a
real division algebra if there are no zero divisors: xy= 0 implies x= 0 or y= 0. By the …

We show that any quasi-polynomial invariant of a quasi-polynomial dynamical system can
be transformed into a quasi-polynomial invariant of a homogeneous quadratic Lotka …

differential equations, dynamical systems, and control science: A Festschrift in Honor of
Lawrence Markus Page 1 9 Differential Systems and Algebras Michael K. Kinyon Indiana …

Since they were introduced by Poincaré and Dulac (and by Birkhoff for Hamiltonian
systems), normal forms have proven to be a valuable tool in the local theory of ordinary …