Valuing American options in the presence of user-defined smiles and time-dependent volatility: scenario analysis, model stress and lower-bound pricing applications

2001 ◽  
Vol 4 (1) ◽  
pp. 35-61 ◽  
Author(s):  
Peter Jäckel ◽  
Riccardo Rebonato
Keyword(s):  
Lower Bound ◽  
Scenario Analysis ◽  
American Options ◽  
Time Dependent ◽  
Analysis Model

Model of vibration in drilling into fibre-reinforced composite materials

2009 ◽  
Vol 223 (9) ◽  
pp. 1107-1114
Author(s):  
B W Huang
Keyword(s):  
Composite Materials ◽  
Vibration Amplitude ◽  
Time Dependent ◽  
Process Time ◽  
Drilling Process ◽  
Improve Product Quality ◽  
Analysis Model ◽  
Inhomogeneous Materials ◽  
Reinforced Composite ◽  
Twisted Beam

A model of the dynamic drill characteristics while drilling through fibre-reinforced composite materials (FRCMs) is investigated in this study. Anisotropic and inhomogeneous materials such as FRCMs, which are used to improve product quality, make it possible to improve production rate and avoid drill breakage. Such materials were used to study the dynamic characteristics of the drilling process. A theoretical analysis model for drilling composite materials is proposed. A pre-twisted beam is used to simulate the drill. A moving Winkler-type elastic foundation is used to approximate the drilling process time-dependent boundary. Numerical analysis indicates that the vibration amplitude changes significantly as the drill moves through composite material.

scholarly journals Ten-year analysis of the risk of severe outcomes related to low-dose glucocorticoids in early Rheumatoid Arthritis

Rheumatology ◽  
2020 ◽  
Author(s):  
Camille Roubille ◽  
Amandine Coffy ◽  
Nathalie Rincheval ◽  
Maxime Dougados ◽  
René-Marc Flipo ◽  
...  
Keyword(s):  
Primary Outcome ◽  
Low Dose ◽  
Univariate Analysis ◽  
Time Dependent ◽  
Cumulative Exposure ◽  
Tolerability Profile ◽  
Analysis Model ◽  
Early Ra ◽  
Severe Infections

Abstract Objectives To explore the 10-year tolerability profile of GC use in patients with early RA. Methods Analysis of 10-year outcome from the early arthritis ESPOIR cohort. Patients were stratified in two groups, without or with GC treatment at least once during their follow-up. The primary outcome was a composite of deaths, cardiovascular diseases (CVD), severe infections and fractures. The weighted Cox time-dependent analysis model was used with inverse probability of treatment weighting (IPTW) propensity score method. Results Among the 608 patients (480 women, mean age of 47.5 ± 12.1 years), 397 (65%) received low-dose GC (median 1.9 mg/day [IQR 0.6–4.2], mean cumulative prednisone dose 8468 mg ±8376, mean duration 44.6 months ± 40.1). In univariate analysis, over 95 total events (10 deaths, 18 CVDs, 32 fractures and 35 severe infections), patients taking GC experienced more events (n = 71) than those without GC (n = 24) (p= 0.035). Highest cumulative exposure of GC (≥8.4 g) was associated with highest risk of occurrence of the primary outcome (24.3%, p= 0.007), CVDs (7.9%, p= 0.001) and severe infections (9.9%, p= 0.024). The risk of events over time was significantly associated with GC, age, hypertension and erythrocyte sedimentation rate. The risk associated with GC treatment increased between the first follow-up visit (HR at 1 year = 0.46, 95% CI 0.23 – 0.90) and 10 years (HR = 6.83, 95% CI 2.29–20.35). Conclusion The 10-year analysis of this prospective early RA cohort supports a dose and time-dependent impact of low-dose GC treatment, with a long-term high risk of severe outcomes. Trial registration (NCT03666091).

Dynamic Discretization Discovery Algorithms for Time-Dependent Shortest Path Problems

2021 ◽  
Author(s):  
Edward Yuhang He ◽  
Natashia Boland ◽  
George Nemhauser ◽  
Martin Savelsbergh
Keyword(s):  
Lower Bound ◽  
Travel Time ◽  
Shortest Path ◽  
Optimal Path ◽  
Upper Bounds ◽  
Shortest Path Problem ◽  
Time Dependent ◽  
Time Interval ◽  
Shortest Path Problems ◽  
Discovery Algorithms

Finding a shortest path in a network is a fundamental optimization problem. We focus on settings in which the travel time on an arc in the network depends on the time at which traversal of the arc begins. In such settings, reaching the destination as early as possible is not the only objective of interest. Minimizing the duration of the path, that is, the difference between the arrival time at the destination and the departure from the origin, and minimizing the travel time along the path from origin to destination, are also of interest. We introduce dynamic discretization discovery algorithms to efficiently solve such time-dependent shortest path problems with piecewise linear arc travel time functions. The algorithms operate on partially time-expanded networks in which arc costs represent lower bounds on the arc travel time over the subsequent time interval. A shortest path in this partially time-expanded network yields a lower bound on the value of an optimal path. Upper bounds are easily obtained as by-products of the lower bound calculations. The algorithms iteratively refine the discretization by exploiting breakpoints of the arc travel time functions. In addition to time discretization refinement, the algorithms permit time intervals to be eliminated, improving lower and upper bounds, until, in a finite number of iterations, optimality is proved. Computational experiments show that only a small fraction of breakpoints must be explored and that the fraction decreases as the length of the time horizon and the size of the network increases, making the algorithms highly efficient and scalable. Summary of Contribution: New data collection techniques have increased the availability and fidelity of time-dependent travel time information, making the time-dependent variant of the classic shortest path problem an extremely relevant problem in the field of operations research. This paper provides novel algorithms for the time-dependent shortest path problem with both the minimum duration and minimum travel time objectives, which aims to address the computational challenges faced by existing algorithms. A computational study shows that our new algorithm is indeed significantly more efficient than existing approaches.

An enhanced lower bound for the Time-Dependent Travelling Salesman Problem

2020 ◽  
Vol 113 ◽  
pp. 104795 ◽  
Author(s):  
Tommaso Adamo ◽  
Gianpaolo Ghiani ◽  
Emanuela Guerriero
Keyword(s):  
Lower Bound ◽  
Travelling Salesman Problem ◽  
Time Dependent ◽  
Travelling Salesman

Does the urban sprawl matter in Yangtze River Economic Belt, China? An integrated analysis with urban sprawl index and one scenario analysis model

Cities ◽  
2020 ◽  
Vol 99 ◽  
pp. 102611 ◽  
Author(s):  
Dongjie Guan ◽  
Xiujuan He ◽  
Chunyang He ◽  
Lidan Cheng ◽  
Sijia Qu
Keyword(s):  
Urban Sprawl ◽  
Scenario Analysis ◽  
Yangtze River ◽  
Integrated Analysis ◽  
Analysis Model

scholarly journals Predictive mathematical models for the number of individuals infected with COVID-19

2020 ◽  
Author(s):  
A.S. Fokas ◽  
N. Dikaios ◽  
G.A. Kastis
Keyword(s):  
Lower Bound ◽  
Mathematical Models ◽  
Closed Form ◽  
Upper Bound ◽  
Logistic Model ◽  
Simple Formula ◽  
Time Dependent ◽  
Sigmoidal Curve ◽  
Specific Virus ◽  
Number Of Individuals

AbstractWe model the time-evolution of the number N(t) of individuals reported to be infected in a given country with a specific virus, in terms of a Riccati equation. Although this equation is nonlinear and it contains time-dependent coefficients, it can be solved in closed form, yielding an expression for N(t) that depends on a function α(t). For the particular case that α(t) is constant, this expression reduces to the well-known logistic formula, giving rise to a sigmoidal curve suitable for modelling usual epidemics. However, for the case of the COVID-19 pandemic, the long series of available data shows that the use of this simple formula for predictions underestimates N(t); thus, the logistic formula only provides a lower bound of N(t). After experimenting with more than 50 different forms of α(t), we introduce two novel models that will be referred to as “rational” and “birational”. The parameters specifying these models (as well as those of the logistic model), are determined from the available data using an error-minimizing algorithm. The analysis of the applicability of the above models to the cases of China and South Korea suggest that they yield more accurate predictions, and importantly that they may provide an upper bound of the actual N(t). Results are presented for Italy, Spain, and France.

Modeling Time-Dependent Pore Pressure Due to Capillary and Chemical Potential Effects and Resulting Wellbore Stability in Shales

2003 ◽  
Vol 125 (3) ◽  
pp. 169-176 ◽  
Author(s):  
M. K. Rahman ◽  
Zhixi Chen ◽  
Sheik S. Rahman
Keyword(s):  
Pore Pressure ◽  
Chemical Potential ◽  
Normal Fault ◽  
Wellbore Stability ◽  
Time Dependent ◽  
Analytical Models ◽  
Analysis Model ◽  
Stress Regime ◽  
Dependent Change ◽  
Drilling Operations

During drilling operations, the mud filtrate interacts with the pore fluid around the wellbore and changes pore pressure by capillary and chemical potential effects. Thus the change in pore pressure around borehole becomes time-dependent, particularly in extremely low permeability shaley formations. In this paper, the change in pore pressure due to capillary and chemical potential effects are investigated experimentally. Analytical models are also developed based on the experimental results. A wellbore stability analysis model incorporating the time-dependent change in pore pressure is applied to a vertical well in a shale formation under normal fault stress regime.

scholarly journals Floyd-A∗Algorithm Solving the Least-Time Itinerary Planning Problem in Urban Scheduled Public Transport Network

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Yu Zhang ◽  
Jiafu Tang ◽  
Shimeng Lv ◽  
Xinggang Luo
Keyword(s):  
Lower Bound ◽  
Real World ◽  
Public Transport ◽  
Ad Hoc ◽  
A Priori ◽  
Time Dependent ◽  
Initial Time ◽  
Planning Problem ◽  
A Algorithm ◽  
Shenyang City

We consider an ad hoc Floyd-A∗algorithm to determine the a priori least-time itinerary from an origin to a destination given an initial time in an urban scheduled public transport (USPT) network. The network is bimodal (i.e., USPT lines and walking) and time dependent. The modified USPT network model results in more reasonable itinerary results. An itinerary is connected through a sequence of time-label arcs. The proposed Floyd-A∗algorithm is composed of two procedures designated as Itinerary Finder and Cost Estimator. The A∗-based Itinerary Finder determines the time-dependent, least-time itinerary in real time, aided by the heuristic information precomputed by the Floyd-based Cost Estimator, where a strategy is formed to preestimate the time-dependent arc travel time as an associated static lower bound. The Floyd-A∗algorithm is proven to guarantee optimality in theory and, demonstrated through a real-world example in Shenyang City USPT network to be more efficient than previous procedures. The computational experiments also reveal the time-dependent nature of the least-time itinerary. In the premise that lines run punctually, “just boarding” and “just missing” cases are identified.

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