科研成果

We propose several methods to obtain endogenous and positive ultimate forward rates (UFRs) for risk-free interest rate curves based on the Smith-Wilson method. The Smith-Wilson method, adopted by Solvency II, can both interpolate the market price data and extrapolate to the UFR. However, it requires an exogenously-chosen UFR. de Kort and Vellekoop (2016) proposed an optimization problem to obtain an endogenous UFR. In this paper, we prove the existence of the optimal endogenous UFR to their optimization problem. In addition, in order to ensure the positiveness of the optimal UFR, we formulate a new optimization framework with nonnegative constraints. Furthermore, we also propose another optimization framework to generate endogenous and positive UFRs with prior knowledge. The feasibilities of both methods are proven under several mild conditions. We use Chinese government bond data to illustrate the capabilities of our methods and find the dynamic behaviour of Chinese risk-free interest rate curves.

This paper explores the socio-political evolution of Amastris, a city in northern Anatolia founded by the Achaemenid princess Amastris in the early 3rd century BCE, with a particular focus on its territorial scope—the Amastriane—during Roman and Hellenistic times. Based on Christian Marek’s reconstruction, the Roman Amastriane stretched far beyond its coastal nucleus, reaching deep into the Paphlagonian interior. This paper investigates whether this expansive territory was a Roman creation or if it echoed earlier Hellenistic configurations, possibly dating back to Amastris or the Mithridatid kings. Section one reviews Marek’s methodological framework, emphasizing the diverse, geographically challenging territory governed by Amastris in Roman times, which required transcending typical coastal-urban dynamics. In section two, epigraphic and archaeological evidence from the Eflani-Pınarbaşı region sheds light on the integration of rural inland communities, highlighting a deep continuity of Macedonian, Achaemenid, and local traditions into the Roman period. Finally, the paper explores whether Amastris’ Hellenistic chora could have reached similar extents, potentially through dowry lands or political marriages rather than military conquest, as suggested by Memnon-in-Photios. The long-lasting cultural ties between coastal and inland Paphlagonia, preserved in cult practices and social structures, point toward a cohesive region predating Roman intervention, raising critical questions about the nature of territorial governance in both Hellenistic and Roman Amastris.