Fake Exponential Brownian Motion

We construct a fake exponential Brownian motion, a continuous martingale different from classical exponential Brownian motion but with the same marginal distributions, thus extending results of Albin and Oleszkiewicz for fake Brownian motions. The ideas extend to other diffusions.Comment: 8 page

The left-curtain martingale coupling in the presence of atoms

Beiglböck and Juillet (Ann. Probab. 44 (2016) 42–106) introduced the left-curtain martingale coupling of probability measures μ and ν, and proved that, when the initial law μ is continuous, it is supported by the graphs of two functions. We extend the later result by constructing the generalised left-curtain martingale coupling and show that for an arbitrary starting law μ it is characterised by two appropriately defined lower and upper functions. As an application of this result, we derive the model-independent upper bound of an American put option. This extends recent results of Hobson and Norgilas (2017) on the atom-free case

An Optimal Skorokhod Embedding for Diffusions

Given a Brownian motion $B_t$ and a general target law $\mu$ (not necessarily centered or even integrable) we show how to construct an embedding of $\mu$ in $B$. This embedding is an extension of an embedding due to Perkins, and is optimal in the sense that it simultaneously minimises the distribution of the maximum and maximises the distribution of the minimum among all embeddings of $\mu$. The embedding is then applied to regular diffusions, and used to characterise the target laws for which a $H^p$-embedding may be found.Comment: 22 pages, 4 figure

Cut Off From(One\u27s) People_Punitive Expulsion In The Torah

Hobson, G. Thomas. “‘Cut Off From (One’s) People’: Punitive Expulsion in the Torah.” Ph.D. diss., Concordia Seminary, 2010. 245 pp. This dissertation argues that the Torah’s penalty “cut off from (one’s) people” (kareth) is normally a form of expulsion from the community of Israel, in contrast to the view that this penalty is a threatened divine extermination curse, a view reflected in the LXX and rabbinic traditions. The author traces a punitive expulsion interpretation from the fifth century B.C.E. Jewish community, to Maccabean-era practice as described by Josephus, to expulsion at Qumran. The use of the verb כדת is examined, including evidence from synonyms and from the Jewish and Samaritan Targumim. Evidence for punitive expulsion elsewhere in the ancient Near East is also assembled. The closest parallels to the biblical kareth penalty are found to be the expulsion of the unclean uzug in early Mesopotamia, and expulsion for the crime of hurkel practiced by the Hittites. Biblical kareth is found to be a merciful alternative to the death penalty, which also removes a source of contamination that endangers the community

An investigation into the heat transfer aspects of transpiration cooling

A dissertation presented in fulfilment of the requirements for the Degree of Master of Science in Engineering DECEMBER 1982Although transpiration cooling has been demonstrated to keep the metal surface temperatures, in a gar turbine, below that at which oxidation occurs even though the hot gas temperatures are in excess of the metals melting temperature, few experimental studies have been conducted on the heat transfer aspects of transpiration cooling. Especially the effect blowing has on a turbulent boundary layer that has developed over a porous surface that is heated by the mainstream. Many studies have involved the blowing or suction oi the boundary layer through heated porous plates. Trans. an cooling was exper cntally investigated by making use of an existing wind tunnel which was modified so as to simulate the heat transfer phenomenon resulting from blowing coolant through a porous wall into a heated mainstream. The existing wind tunnel was designed and commissioned by Krieg (13) who considered the momentum transfer aspects of transpiration cooling. The solution of the momentum equation by Krieg forms the basis from which this investigation was developed, the original solution procedure being put forward by Cebeci and Smith (7). Krieg developed a generalised two-dimensional finite-differunce compute* program to solve the incompressible momentum equations describing a blown boundary layer. This program was further developed as part of this effort to solve the compressible momentum and neigy equations so as to account for the heat transfer in the blown boundary layer. The program is used to predict the experimental results obtained from the literature as well is those ottained during the nine experimental runs on the wind tunnel. Freestream flow velocities varied from 4,^5 m/s to 14,95 m/s with correspoi ;.ng temperatures of 44,95°C and 33,00eC respectively. The blowing fr tion F, was varied from 0,0059 to a maximum of , temperature of 40°C. The numerically calculated profiles and tho: » obi lined expurim ntally, as well as one set presented by another researcher, compared well. Finally, recommendations for future studies have been suggested

Root to Kellerer

We revisit Kellerer's Theorem, that is, we show that for a family of real probability distributions $(\mu_t)_{t\in [0,1]}$ which increases in convex order there exists a Markov martingale $(S_t)_{t\in[0,1]}$ s.t.\ $S_t\sim \mu_t$. To establish the result, we observe that the set of martingale measures with given marginals carries a natural compact Polish topology. Based on a particular property of the martingale coupling associated to Root's embedding this allows for a relatively concise proof of Kellerer's theorem. We emphasize that many of our arguments are borrowed from Kellerer \cite{Ke72}, Lowther \cite{Lo07}, and Hirsch-Roynette-Profeta-Yor \cite{HiPr11,HiRo12}.Comment: 8 pages, 1 figur

Integrability of solutions of the Skorokhod embedding problem for diffusions

Suppose X is a time-homogeneous diffusion on an interval IX⊆R and let μ be a probability measure on IX. Then τ is a solution of the Skorokhod embedding problem (SEP) for μ in X if τ is a stopping time and Xτ∼μ. There are well-known conditions which determine whether there exists a solution of the SEP for μ in X. We give necessary and sufficient conditions for there to exist an integrable solution. Further, if there exists a solution ofthe SEP then there exists a minimal solution. We show that every minimal solution of the SEP has the same first moment. When X is Brownian motion, there exists an integrable embedding of μ if and only if μ is centred and in L2. Further,every integrable embedding is minimal. When X is a general time-homogeneous diffusion the situation is more subtle. The case with drift can be reduced to the local martingale case by a change of scale. If Y is a diffusion in natural scale, and if the target law is centred, then as in the Brownian case, there is an integrable embedding if the target law satisfies an integral condition. However, unlike in the Brownian case, there exist integrable embeddings of target laws which are not centred. Further, there exist integrable embeddings which are not minimal. Instead, if there exists an integrable embedding, then the set of minimal embeddings is the set of embeddings such that the mean equals a certain quantity, which we identify

Optimal consumption and sale strategies for a risk averse agent

In this article we consider a special case of an optimal consumption/optimal portfolio problem first studied by Constantinides and Magill and by Davis and Norman, in which an agent with constant relative risk aversion seeks to maximise expected discounted utility of consumption over the infinite horizon, in a model comprising a risk-free asset and a risky asset with proportional transaction costs. The special case that we consider is that the cost of purchases of the risky asset is infinite, or equivalently the risky asset can only be sold and not bought. In this special setting new solution techniques are available, and we can make considerable progress towards an analytical solution. This means we are able to consider the comparative statics of the problem. There are some surprising conclusions, such as consumption rates are not monotone increasing in the return of the asset, nor are the certainty equivalent values of the risky positions monotone in the risk aversion