Related papers: On Finite-dimensional Term Structure models

In this paper, an algebraic theory for local rings of finite embedding dimension is developed. Several extensions of (Krull) dimension are proposed, which are then used to generalize singularity notions from commutative algebra. Finally,…

This work is devoted to a systematic study of symplectic convexity for integrable Hamiltonian systems with elliptic and focus-focus singularities. A distinctive feature of these systems is that their base spaces are still smooth manifolds…

We study the long-time behavior of affine processes on positive self-adjoiont Hilbert-Schmidt operators which are of pure-jump type, conservative and have finite second moment. For subcritical processes we prove the existence of a unique…

We continue the study of non-invertible topological dynamical systems with expanding behavior. We introduce the class of {\em finite type} systems which are characterized by the condition that, up to rescaling and uniformly bounded…

In this paper, we study term structure movements in the spirit of Heath, Jarrow, and Morton [Econometrica 60(1), 77-105] under volatility uncertainty. We model the instantaneous forward rate as a diffusion process driven by a G-Brownian…

The Convolution and Master equations governing the time behavior of the term structure of Interest Rates are set up both for continuous variables and for their discretised forms. The notion of Seed is introduced. The discretised theoretical…

We study the infinitesimal variation of Hodge structure associated with families of reduced algebraic curves with singularities. The analysis applies to curves beyond the nodal case and is not restricted to plane curves, encompassing curves…

We define the continuous modeling property for first-order structures and show that a first-order structure has the continuous modelling property if and only if its age has the embedding Ramsey property. We use generalized indiscernible…

We give sufficient conditions which ensure that a functor of finite length from an additive category to finite-dimensional vector spaces has a projective resolution whose terms are finitely generated. For polynomial functors, we study also…

The affine Gaudin model, associated with an untwisted affine Kac-Moody algebra, is known to arise from a certain gauge fixing of 4-dimensional mixed topological-holomorphic Chern-Simons theory in the Hamiltonian framework. We show that the…

We present compelling empirical evidence for a new interpretation of the Forward Rate Curve (FRC) term structure. We find that the average FRC follows a square-root law, with a prefactor related to the spot volatility, suggesting a…

I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of…

In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox-Ingersoll-Ross two factors model describing clustering of…

For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties. We also study their limits when the…

We construct a finite element like scheme for fully non-linear integro-partial differential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in…

The objects of study in this paper are Hopf algebras $H$ which are finitely generated algebras over an algebraically closed field and are extensions of a commutative Hopf algebra by a finite dimensional Hopf algebra. Basic structural and…

We develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions. The family contains elements of all polynomial degrees and all form degrees. In two dimensions, these include the…

In this paper we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting times of jumps can be both inaccessible and predictable. To this end we develop a general theory of finite…

We use the theory of cubic structures to give a fixed point Riemann-Roch formula for the equivariant Euler characteristics of coherent sheaves on projective flat schemes over Z with a tame action of a finite abelian group. This formula…

Finite element de Rham complexes and finite element Stokes complexes with various smoothness in three dimensions are systematically constructed. First smooth scalar finite elements in three dimensions are derived through a non-overlapping…