This article assembles the evidence for the presence of Greek refugees in early modern Scotland. These refugees came in two distinct waves: one in the aftermath of the fall of Constantinople in 1453, and another in the seventeenth century. In both periods, inter-regional religious networks brought Greeks to Scotland: in the first phase, these were structured around the church institutions of the Latin West; in the second, they followed ecumenical interest in Protestant Northern Europe. The wanderers were mostly clergymen. This movement of refugees, alongside the capture of Scots by North African corsairs, linked Scotland with the distant Ottoman world.

With the reinstatement of the parliament in 1908, the Ottoman state faced new challenges connected to citizenship. As a policy to finally make citizens equal in rights as well as duties, military conscription figured prominently in this new context. For the first time in Ottoman history, the empire's non-Muslims began to be drafted en masse. This article explores meanings of imperial citizenship and equality through the lens of debates over the conscription of Greek Ottomans, the largest non-Muslim population of the Ottoman Empire. In contrast to the widespread suggestion of the Turkish nationalist historiography on these matters, Greek Ottomans and other non-Muslim populations enthusiastically supported the military service in principle. But amidst this general agreement was a tremendous array of views on what conscription ought to look like in practice. The issue came to center on whether Greek Ottomans should have separate battalions in the army. All units would eventually come to be religiously integrated, but the conscription debates in the Ottoman parliament as well as in the Turkish and Greek language press reveal some of the crucial fissures of an empire as various actors were attempting to navigate between a unified citizenship and a diverse population.

In the Gospel of John, the apostles Andrew and Philip enjoy a privileged position right from the beginning. The reason seems to lie in the fact that they, being from Bethsaida in Galilee and probably fluent in Greek, could serve as intermediaries between ‘Greeks’ and Jesus, whom they wanted to ‘see’. Such an encounter happens in John 12.20–2. According to John, Jesus called Andrew before his brother Peter, whom Andrew then led to Jesus. Philip is the second person directly called by Jesus, himself leading another future disciple to Jesus: Nathanael (John 1.35–46). James and John are completely missing not only in the Johannine scene of the calling of disciples but also in the whole of the Fourth Gospel. The importance of Andrew and Philip follows also from the rest of the Gospel of John. The evangelist seems to depend on an early tradition attested in Asia Minor and to modify the synoptic tradition on its basis.

This paper is devoted to the American option pricing problem governed by the Black-Scholes equation. The existence of an optimal exercise policy makes the problem a free boundary value problem of a parabolic equation on an unbounded domain. The optimal exercise boundary satisfies a nonlinear Volterra integral equation and is solved by a high-order collocation method based on graded meshes. This free boundary is then deformed to a fixed boundary by the front-fixing transformation. The boundary condition at infinity (due to the fact that the underlying asset's price could be arbitrarily large in theory), is treated by the perfectly matched layer technique. Finally, the resulting initial-boundary value problems for the option price and some of the Greeks on a bounded rectangular space-time domain are solved by a finite element method. In particular, for Delta, one of the Greeks, we propose a discontinuous Galerkin method to treat the discontinuity in its initial condition. Convergence results for these two methods are analyzed and several numerical simulations are provided to verify these theoretical results.

The implementation of hedging strategies for variable annuity products requires the calculation of market risk sensitivities (or “Greeks”). The complex, path-dependent nature of these products means that these sensitivities are typically estimated by Monte Carlo methods. Standard market practice is to use a “bump and revalue” method in which sensitivities are approximated by finite differences. As well as requiring multiple valuations of the product, this approach is often unreliable for higher-order Greeks, such as gamma, and alternative pathwise (PW) and likelihood-ratio estimators should be preferred. This paper considers a stylized guaranteed minimum withdrawal benefit product in which the reference equity index follows a Heston stochastic volatility model in a stochastic interest rate environment. The complete set of first-order sensitivities with respect to index value, volatility and interest rate and the most important second-order sensitivities are calculated using PW, likelihood-ratio and mixed methods. It is observed that the PW method delivers the best estimates of first-order sensitivities while mixed estimation methods deliver considerably more accurate estimates of second-order sensitivities; moreover there are significant computational gains involved in using PW and mixed estimators rather than simple BnR estimators when many Greeks have to be calculated.

The focus of this paper is the identification, and more importantly, sustainable management, of risks embedded in guarantees attaching to unit linked savings and retirement contracts (as commonly referred to as GMxBs). In developing customer centric guarantees that are not readily transferrable to the capital markets, insurance undertakings require the skills and resources to hedge the guarantees within their own balance sheet (or with a temporary use of packaged solutions such as reinsurance). In taking on the guarantee manufacture task insurers are departing from areas of historic competence and need to develop a comprehensive understanding of all elements of market risk replication. These include both first order market exposures as well as the material second order risks associated with market micro structure. The paper seeks to integrate this comprehensive analysis within a practitioner focused framework and concludes with a senior executive summary of “Seven key considerations in successful guarantee manufacture”.

T.J. Dunbabin's book The western Greeks was published 50 years ago. In it he modelled the development of the Greek cities of Italy on the British Empire of the 1930s. Here Franco De Angelis explores the problem of faulty and distorting analogies.