The tag has no wiki summary.

learn more… | top users | synonyms

6
votes
5answers
2k views

Discrete version of Ito's lemma

Could anyone give me some references where I could find (a) discrete version(s) of Ito's lemma (b) a proof how it converges to the continuous form in the limit (c) its usage within stochastic ...
2
votes
1answer
323 views

Moment Generating Function: Pulling a term out of k-times differentiation

In Wiersema: Brownian Motion Calculus on p. 205 (in an Annex on Moment Generating Functions (mgf)) the following equation is being presented $${d^k \over d\theta^k} \left ({1\over ...
1
vote
2answers
494 views

Exploding Levy processes

Hi, probably this is a fairly newbie question, but is it possible that the a generic Levy process explodes (i.e. tends to infinity for finite time t with positive probability)? If yes, could you ...
1
vote
1answer
250 views

Extension of some feature of SDE Ornstein-Uhlenbeck type

Hi everyone, I am looking for some ideas (or references) in order to get an explicit SDE (if it exists) which would have a stylised property extending in some sense the mean-reversion property of SDE ...
0
votes
2answers
294 views

Units in Ornstein-Uhlenbeck(OU) process

Take an OU process characterized by X(0) = x dX(t) = - a X(t) dt + b dW(t) where a,b >0. The parameter a is usually interpreted a dissipative term, and b is a ...
9
votes
2answers
521 views

Inequality in Gaussian space — possibly provable by rearrangement?

The following problem arose for my collaborators and me when studying the computational complexity of the Maximum-Cut problem. Let $f : \mathbb{R} \to \mathbb{R}$ be an odd function. Let $\rho \in ...
1
vote
4answers
363 views

CAS for finding closed form solutions to PDEs and SDEs?

Are there any specialized Computer Algebra Systems (or packages for these) for finding closed form solutions to a) partial differential equations, b) stochastic differential equations? If yes, what ...
3
votes
2answers
467 views

maximizing function (stochastic calculus)

S is a price process which follows Geometric Brownian motion with no drift: dS=S*vol*dW, vol=const., W is a Wiener process. Define the following ratio: R=E[Max(f(S)-S(T),0)]/E[f(S)], where S(T) is ...