Decomposing and valuing callable convertible bonds: a new method based on exotic options

In the framework of Black-Scholes-Merton option pricing models, by employing exotic options instead of plain options or warrants, this paper presents an equivalent decomposition method for usual Callable Convertible Bonds (CCB). Furthermore, the analytic valuation formulae for CCB are worked out by using the analytic formulae for those simpler securities decomposed from CCB. Moreover, this method is validated by comparing with Monte Carlo simulation. Besides, the effects of call clauses, coupon clauses and soft call condition clauses are analyzed respectively. These give lots of new insights into the valuation and analysis of CCB and much help to hedge their risks.Callable convertible bonds; Equivalent decomposition; Up-and-out calls; American binary calls; Derivative pricing

NavGPT: Explicit Reasoning in Vision-and-Language Navigation with Large Language Models

Trained with an unprecedented scale of data, large language models (LLMs) like ChatGPT and GPT-4 exhibit the emergence of significant reasoning abilities from model scaling. Such a trend underscored the potential of training LLMs with unlimited language data, advancing the development of a universal embodied agent. In this work, we introduce the NavGPT, a purely LLM-based instruction-following navigation agent, to reveal the reasoning capability of GPT models in complex embodied scenes by performing zero-shot sequential action prediction for vision-and-language navigation (VLN). At each step, NavGPT takes the textual descriptions of visual observations, navigation history, and future explorable directions as inputs to reason the agent's current status, and makes the decision to approach the target. Through comprehensive experiments, we demonstrate NavGPT can explicitly perform high-level planning for navigation, including decomposing instruction into sub-goal, integrating commonsense knowledge relevant to navigation task resolution, identifying landmarks from observed scenes, tracking navigation progress, and adapting to exceptions with plan adjustment. Furthermore, we show that LLMs is capable of generating high-quality navigational instructions from observations and actions along a path, as well as drawing accurate top-down metric trajectory given the agent's navigation history. Despite the performance of using NavGPT to zero-shot R2R tasks still falling short of trained models, we suggest adapting multi-modality inputs for LLMs to use as visual navigation agents and applying the explicit reasoning of LLMs to benefit learning-based models

Well-posedness of the discrete nonlinear Schr\"odinger equations and the Klein-Gordon equations

The primary objective of this paper is to investigate the well-posedness theories associated with the discrete nonlinear Schr\"odinger equation and Klein-Gordon equation. These theories encompass both local and global well-posedness, as well as the existence of blowing-up solutions for large and irregular initial data. The main results of this paper presented in this paper can be summarized as follows: 1. Discrete Nonlinear Schr\"odinger Equation: We establish global well-posedness in $l^p_h$ spaces for all $1\leq p\leq \infty$, regardless of whether it is in the defocusing or focusing cases. 2. Discrete Klein-Gordon Equation (including Wave Equation): We demonstrate local well-posedness in $l^p_h$ spaces for all $1\leq p\leq \infty$. Furthermore, in the defocusing case, we establish global well-posedness in $l^p_h$ spaces for any $2\leq p\leq 2\sigma+2$. In contrast, in the focusing case, we show that solutions with negative energy blow up within a finite time

A molecular simulation analysis of producing monatomic carbon chains by stretching ultranarrow graphene nanoribbons

Atomistic simulations were utilized to develop fundamental insights regarding the elongation process starting from ultranarrow graphene nanoribbons (GNRs) and resulting in monatomic carbon chains (MACCs). There are three key findings. First, we demonstrate that complete, elongated, and stable MACCs with fracture strains exceeding 100% can be formed from both ultranarrow armchair and zigzag GNRs. Second, we demonstrate that the deformation processes leading to the MACCs have strong chirality dependence. Specifically, armchair GNRs first form DNA-like chains, then develop into monatomic chains by passing through an intermediate configuration in which monatomic chain sections are separated by two-atom attachments. In contrast, zigzag GNRs form rope-ladder-like chains through a process in which the carbon hexagons are first elongated into rectangles; these rectangles eventually coalesce into monatomic chains through a novel triangle-pentagon deformation structure under further tensile deformation. Finally, we show that the width of GNRs plays an important role in the formation of MACCs, and that the ultranarrow GNRs facilitate the formation of full MACCs. The present work should be of considerable interest due to the experimentally demonstrated feasibility of using narrow GNRs to fabricate novel nanoelectronic components based upon monatomic chains of carbon atoms.Comment: 11 pages, 6 figures, Nanotechnology accepted versio