Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance

In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain is convergent of first order in the timestep and second order in the spatial grid size, and that the discretisation is stable with respect to boundary data. Numerical experiments clearly indicate that the same convergence order also holds for boundary-value problems. Multilevel path simulation, previously used for SDEs, is shown to give substantial complexity gains compared to a standard discretisation of the SPDE or direct simulation of the particle system. We derive complexity bounds and illustrate the results by an application to basket credit derivatives

Executive stock option exercise with full and partial information on a drift change point

We analyse the optimal exercise of an executive stock option (ESO) written on a stock whose drift parameter falls to a lower value at a change point, an exponentially distributed random time independent of the Brownian motion driving the stock. Two agents, who do not trade the stock, have differing information on the change point, and seek to optimally exercise the option by maximising its discounted payoff under the physical measure. The first agent has full information, and observes the change point. The second agent has partial information and filters the change point from price observations. This scenario is designed to mimic the positions of two employees of varying seniority, a fully informed executive and a partially informed less senior employee, each of whom receives an ESO. The partial information scenario yields a model under the observation filtration $\widehat{\mathbb{F}}$ in which the stock drift becomes a diffusion driven by the innovations process, an $\widehat{\mathbb{F}}$-Brownian motion also driving the stock under $\widehat{\mathbb{F}}$, and the partial information optimal stopping value function has two spatial dimensions. We rigorously characterise the free boundary PDEs for both agents, establish shape and regularity properties of the associated optimal exercise boundaries, and prove the smooth pasting property in both information scenarios, exploiting some stochastic flow ideas to do so in the partial information case. We develop finite difference algorithms to numerically solve both agents' exercise and valuation problems and illustrate that the additional information of the fully informed agent can result in exercise patterns which exploit the information on the change point, lending credence to empirical studies which suggest that privileged information of bad news is a factor leading to early exercise of ESOs prior to poor stock price performance.Comment: 48 pages, final version, accepted for publication in SIAM Journal on Financial Mathematic

Convergence of policy gradient methods for finite-horizon stochastic linear-quadratic control problems

We study the global linear convergence of policy gradient (PG) methods for finite-horizon exploratory linear-quadratic control (LQC) problems. The setting includes stochastic LQC problems with indefinite costs and allows additional entropy regularisers in the objective. We consider a continuous-time Gaussian policy whose mean is linear in the state variable and whose covariance is state-independent. Contrary to discrete-time problems, the cost is noncoercive in the policy and not all descent directions lead to bounded iterates. We propose geometry-aware gradient descents for the mean and covariance of the policy using the Fisher geometry and the Bures-Wasserstein geometry, respectively. The policy iterates are shown to satisfy an a-priori bound, and converge globally to the optimal policy with a linear rate. We further propose a novel PG method with discrete-time policies. The algorithm leverages the continuous-time analysis, and achieves a robust linear convergence across different action frequencies. A numerical experiment confirms the convergence and robustness of the proposed algorithm.Comment: 2 figure

Push and pull escape travel motivations of Emirati nationals to Australia

© 2017, © Emerald Publishing Limited. Purpose: The purpose of this study is to examine the escape motivations of the emerging market and provide suggestions for Australia’s promotion. This study adopts the push and pull framework to identify travel motivations of Emirati nationals to Australia. Design/methodology/approach: This study uses a series of focus groups and in-depth interviews to understand the escape motivations that encourage Emiratis to leave their home country and travel to Australia for a holiday. Findings: The results indicate that Emiratis are motivated to travel to Australia by three escape factors: physical, interpersonal and fun. The internal motivations that encourage Emiratis to escape their home country are inseparable from Australia’s external attributes that attract the Emiratis to the country. Originality/value: The study contributes to the theory of tourist motivation by supporting it in the culturally different Muslim/Arab context, which has not been explored before. The authors argue that it is not so much what Australia offers and what escape needs the Emiratis can fulfil in Australia, but rather that Australia serves the Emiratis well and meets their escape needs

Mycotoxin occurrence in maize silage : a neglected risk for bovine gut health?

Forages are important components of dairy cattle rations but might harbor a plethora of mycotoxins. Ruminants are considered to be less susceptible to the adverse health effects of mycotoxins, mainly because the ruminal microflora degrades certain mycotoxins. Yet, impairment of the ruminal degradation capacity or high ruminal stability of toxins can entail that the intestinal epithelium is exposed to significant mycotoxin amounts. The aims of our study were to assess (i) the mycotoxin occurrence in maize silage and (ii) the cytotoxicity of relevant mycotoxins on bovine intestinal cells. In total, 158 maize silage samples were collected from European dairy cattle farms. LC-MS/MS-based analysis of 61 mycotoxins revealed the presence of emerging mycotoxins (e.g., emodin, culmorin, enniatin B1, enniatin B, and beauvericin) in more than 70% of samples. Among the regulated mycotoxins, deoxynivalenol and zearalenone were most frequently detected (67.7%). Overall, 87% of maize silages contained more than five mycotoxins. Using an in vitro model with calf small intestinal epithelial cells B, the cytotoxicity of deoxynivalenol, nivalenol, fumonisin B1 and enniatin B was evaluated (0-200 mu M). Absolute IC50 values varied in dependence of employed assay and were 1.2-3.6 mu M, 0.8-1.0 mu M, 8.6-18.3 mu M, and 4.0-6.7 mu M for deoxynivalenol, nivalenol, fumonisin B1, and enniatin B, respectively. Results highlight the potential relevance of mycotoxins for bovine gut health, a previously neglected target in ruminants

The UAE\u27s tourism competitiveness: A business perspective

© 2019 Elsevier Ltd The United Arab Emirates (UAE) is one of the most popular tourism destinations and the most competitive in the Middle East and North Africa region. Currently, the country aims to reach its full potential to better compete on a global scale. This paper examines factors influencing the competitiveness of the UAE as a tourism destination from the business perspective. The data were collected from a convenience sample of 311 business entrepreneurs and analyzed using a hierarchical regression. The results suggest that destination resources, destination infrastructure and support services, and the general business environment have a significant influence on the UAE\u27s tourism competitiveness. The implications of the study\u27s results are discussed

Capturing the Dynamics of Ti Diffusion Across Ti _x W _1−x /Cu Heterostructures using X‐Ray Photoelectron Spectroscopy

Interdiffusion phenomena between adjacent materials are highly prevalent in semiconductor device architectures and can present a major reliability challenge for the industry. To fully capture these phenomena, experimental approaches must go beyond static and post-mortem studies to include in situ and in-operando setups. Here, soft and hard X-ray photoelectron spectroscopy (SXPS and HAXPES) is used to monitor diffusion in real-time across a proxy device. The device consists of a Si/SiO2/TixW1−x(300 nm)/Cu(25 nm) thin film material stack, with the TixW1−x film (x = 0.054, 0.115, 0.148) acting as a diffusion barrier between Si and Cu. The interdiffusion is monitored through the continuous collection of spectra whilst in situ annealing to 673 K. Ti within the TiW is found to be highly mobile during annealing, diffusing out of the barrier and accumulating at the Cu surface. Increasing the Ti concentration within the TixW1−x film increases the quantity of accumulated Ti, and Ti is first detected at the Cu surface at temperatures as low as 550 K. Surprisingly, at low Ti concentrations (x = 0.054), W is also mobile and diffuses alongside Ti. By monitoring the Ti 1s core level with HAXPES, the surface-accumulated Ti was observed to undergo oxidation even under ultra-high vacuum conditions, highlighting the reactivity of Ti in this system. These results provide crucial evidence for the importance of diffusion barrier composition on their efficacy during device application, delivering insights into the mechanisms underlying their effectiveness and limitations

μ2-Acetone-diacetone[μ3-tris­(trifluoro­meth­yl)methano­lato]bis­[μ2-tris­(trifluoro­meth­yl)methano­lato]trilithium

The title compound, [Li3(C4F9O)3(C3H6O)3], features an open Li/O cube with an Li ion missing at one corner. Three of the four bridging O atoms of the cube carry a fluorinated tert-butyl residue, whereas the fourth is part of an acetone mol­ecule. Two of the Li atoms are further bonded to a non-bridging acetone mol­ecule. Two of the lithium ion coordination geometries are very distorted LiO4 tetra­hedra; the third could be described as a very distorted LiO3 T-shape with two distant F-atom neighbours. The Li⋯Li contact distances for the three-coordinate Li+ ion [2.608 (14) and 2.631 (12) Å] are much shorter that the contact distance [2.940 (13) Å] between the tetra­hedrally coordinated species