• Corpus ID: 18564769

A Generalized Backward Equation For One Dimensional Processes

@article{Lowther2008AGB,
  title={A Generalized Backward Equation For One Dimensional Processes},
  author={George Lowther},
  journal={arXiv: Probability},
  year={2008}
}
  • G. Lowther
  • Published 23 March 2008
  • Mathematics
  • arXiv: Probability
Suppose that a real valued process X is given as a solution to a stochastic differential equation. Then, for any twice continuously differentiable function f, the backward Kolmogorov equation gives a condition for f(t,X) to be a local martingale. We generalize the backward equation in two main ways. First, it is extended to non-differentiable functions. Second, the process X is not required to satisfy an SDE. Instead, it is only required to be a quasimartingale satisfying an integrability… 

Fitting Martingales To Given Marginals

We consider the problem of finding a real valued martingale fitting specified marginal distributions. For this to be possible, the marginals must be increasing in the convex order and have constant

From Bachelier to Dupire via optimal transport

Famously, mathematical finance was started by Bachelier in his 1900 PhD thesis where – among many other achievements – he also provided a formal derivation of the Kolmogorov forward equation. This

References

SHOWING 1-10 OF 15 REFERENCES

Properties of Expectations of Functions of Martingale Diffusions

Given a real valued and time-inhomogeneous martingale diffusion X, we investigate the properties of functions defined by the conditional expectation f(t,X_t)=E[g(X_T)|F_t]. We show that whenever g is

Nondifferentiable functions of one-dimensional semimartingales

We consider decompositions of processes of the form Y = f(t, X t ) where X is a semimartingale. The function f is not required to be differentiable, so Ito's lemma does not apply. In the case where

Multidimensional Diffusion Processes

Preliminary Material: Extension Theorems, Martingales, and Compactness.- Markov Processes, Regularity of Their Sample Paths, and the Wiener Measure.- Parabolic Partial Differential Equations.- The

Diffusions, Markov processes, and martingales

This celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first,

On Non-Continuous Dirichlet Processes

It is proved that non-continuous Dirichlet processes are stable under C1 transformation.

Variation conditionnelle des processus stochastiques

On considere (Ω, #7B-F, P (#7B-F t ) 0 ≤t≤1) un espace probabilise filtre verifiant les conditions habituelles. (X t ) 0 ≤t≤1 est un processus cadlaz adapte et integrable. On etend des resultats

Stochastic integration and differential equations, volume 21 of Applications of Mathematics (New York)

  • Springer-Verlag, Berlin, second edition,
  • 2004

Stochastic integration and differential equations, volume 21 of Applications of Mathematics

  • Stochastic Modelling and Applied Proba- bility
  • 2004

Semimartingale Theory and Stochastic Calculus

PRELIMINARIES. Monotone Class Theorems. Uniform Integrability. Essential Supremum. The Generalization of Conditional Expectation. Analytic Sets and Choquet Capacity. Lebesgue-Stieltjes Integrals.

Lectures on Lipschitz analysis, volume 100 of Report

  • University of Jyväskylä Department of Mathematics and Statistics. University of Jyväskylä, Jyväskylä,
  • 2005