Related papers: From multi-dimensional black scholes to Hamilton j…
We develop the relation between de Sitter holography and inflation in detail, with particular attention to cosmic density perturbations. We set up the Hamilton-Jacobi formalism to present a systematic treatment of the logarithmic…
A class of one dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra.…
This work is devoted to the study of optimal control of stochastic functional differential equations (SFDEs) and its application to mathematical finance. By using the Dynkin formula and solution of the Dirichlet-Poisson problem, the…
The partial Hamiltonian systems of the form $\dot q^i=\frac{\partial H}{\partial p_i}, \dot p^i=-\frac{\partial H}{\partial q_i}+\Gamma^i(t,q^i,p_i)$ arise widely in different fields of the applied mathematics. The partial Hamiltonian…
The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled…
Hamiltonian formulation of N=3 systems is considered in general. The Jacobi equation is solved in three classes. Compatible Poisson structures in these classes are determined and explicitly given. The corresponding bi-Hamiltonian systems…
Financial markets have developed a lot of strategies to control risks induced by market fluctuations. Mathematics has emerged as the leading discipline to address fundamental questions in finance as asset pricing model and hedging…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
High frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well stablished by empirical evidence. Specifically, probability distributions have the following…
A Hamiltonian analysis of models given by a three-form field with a generic potential coupled to general relativity in four dimensions is performed. This kind of fields are naturally present in string theory and cosmological scenarios. In…
A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new…
The Hamilton-Jacobi approach is a powerful tool to describe super-Hubble dynamics during cosmological inflation in a non-linear way. A key assumption of this framework is to neglect anisotropic perturbations on large scales. We show that…
We consider the problem of time-optimal path planning for simple nonholonomic vehicles. In previous similar work, the vehicle has been simplified to a point mass and the obstacles have been stationary. Our formulation accounts for a…
In this paper we propose an overview of the recent academic literature devoted to the applications of Hawkes processes in finance. Hawkes processes constitute a particular class of multivariate point processes that has become very popular…
We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those…
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
We use the Hamilton-Jacobi theory to study the nonlinear evolutions of inhomogeneous spacetimes during inflation in generalized gravity. We find the exact solutions to the lowest order Hamilton-Jacobi equation for special scalar potentials…
The modeling of financial markets as disequilibrium models by ordinary differential equations has become a popular modeling tool. One famous example of such a model is the Beja-Goldman model(The Journal of Finance, 1980) which we consider…
We extend the now classic structural credit modeling approach of Black and Cox to a class of "two-factor" models that unify equity securities such as options written on the stock price, and credit products like bonds and credit default…
This mini-course provides a presentation of the method of characteristics to initial/boundary-value problems for systems of first-order partial differential equations and to Hamilton-Jacobi variational inequalities. In particular, these…