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Hamza-Klebaner posed the problem of constructing martingales with Brownian marginals that differ from Brownian motion, so called fake Brownian motions. Besides its theoretical appeal, the problem represents the quintessential version of the ubiquitou
Externí odkaz:
http://arxiv.org/abs/2109.12927
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Akademický článek
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Autor:
Lowther, George Edward
We consider the problem of pricing and hedging general path dependent derivatives on a single asset, supposing that we already know the prices of the vanilla options. If we are to avoid introducing arbitrage possibilities, then this is the same as fi
Externí odkaz:
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624374
Formalizing an old desire of Einstein, "psi-epistemic theories" try to reproduce the predictions of quantum mechanics, while viewing quantum states as ordinary probability distributions over underlying objects called "ontic states." Regardless of one
Externí odkaz:
http://arxiv.org/abs/1303.2834
Autor:
Lowther, George
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 mean. We show that, under the extra condition that t
Externí odkaz:
http://arxiv.org/abs/0808.2319
Autor:
Lowther, George
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
Externí odkaz:
http://arxiv.org/abs/0803.3303
Autor:
Lowther, George
Publikováno v:
Annals of Probability 2010, Vol. 38, No. 1, 76-101
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 It\^{o}'s lemma does not apply. In the case where $f(t,x)$ is independent of $t$, it is shown th
Externí odkaz:
http://arxiv.org/abs/0802.0331
Autor:
Lowther, George
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 monotonic or Lipschitz continuous then f(t,x) will
Externí odkaz:
http://arxiv.org/abs/0801.0330
Autor:
Lowther, George
Publikováno v:
Ann. Probab. Volume 37, Number 1 (2009), 78-106
In this paper we look at the properties of limits of a sequence of real valued time inhomogeneous diffusions. When convergence is only in the sense of finite-dimensional distributions then the limit does not have to be a diffusion. However, we show t
Externí odkaz:
http://arxiv.org/abs/0712.2428