金融领域的随机建模与基于软件R的Monte Carlo模拟(4):随机微分方程模型

主要研究线性随机微分方程模型,为此定义Itô随机微积分,建立Itô公式.鉴于研究的重点是利用R软件进行数值模拟,所以详细讨论了过去10多年来随机微分方程数值解的研究.     

金融领域的随机建模与基于软件R的Monte Carlo模拟(2):Cox-Ross-Rubinstein模型

主要讨论了 Cox-Ross-Rubinstein (CRR) 模型和广义的CRR模型,并研究了如何基于CRR模型和广义的CRR模型利用Monte Carlo模拟计算资产价格以及期权价值.     

金融领域的随机建模与基于软件R的Monte Carlo模拟(1):金融期权

为了让更多人了解期权及其相关金融衍生品,论文系统地介绍了金融数学中一些描述资产行为的经典模型,并从数学与计算机仿真的角度,由浅入深地介绍期权定价的计算方法.首先介绍了欧式期权及其研究的必要性,并给出了相关的金融名词的解释,最后估计了期权价值的上下界.     

金融领域的随机建模与基于软件R的Monte Carlo模拟(5):Black-Scholes的世界

主要研究了Black-Scholes模型.与Black-Scholes期权定价公式相比,将再次强调和证实利用R软件Monte Carlo模拟的强大作用.     

金融领域的随机建模与基于软件R的MonteCarlo模拟(3):随机对数线性模型

主要研究了随机对数线性(SLL)模型以及如何基于SLL模型计算欧式期权平均收益.此外,还演绎了资产价格的Monte Carlo模拟.     

Surface energy balance complexity in GCM land surface models. Part II: coupled simulations

 Global coupled simulations with the Bureau of Meteorology Research Centre climate model and the CHAmeleon Surface Model (CHASM) are used to examine how four general extensions to the representation of the basic land surface energy balance affect simulated land-atmosphere interface variables: evaporation, precipitation, skin temperature and air temperature. The impacts of including separate surface energy balance calculations for: vegetated and non-vegetated portions of the land surface; an explicit parametrisation of canopy resistance; explicit bare ground evaporation; and explicit canopy interception are isolated and quantified. The hypothesis that these aspects of surface energy balance parametrisation do not contain substantial information at the monthly time scale (and are therefore not important to consider in a land surface model) is shown to be false. Considerable sensitivity to each of the four general surface energy balance extensions is identified in average pointwise monthly changes for important land-atmosphere interface variables. Average pointwise changes in monthly precipitation and land evaporation are equal to about 40 and 31–37% of the global-average precipitation and land evaporation respectively. Average pointwise changes for land surface skin temperature and lowest model layer air temperature are about 2 and 0.9 K respectively. The average pointwise change and average pointwise biases are statistically significant at 95% in all cases. Substantial changes to zonally average variables are also identified. We demonstrate how the globally averaged surface resistance parameter can vary from 150 to 25 s/m depending on which aspects of the surface energy balance are treated implicitly. We also show that if interception is treated implicitly, the effective surface resistance must vary geographically in order to capture the behaviour of a model which treats this process explicitly. The implication of these results for the design of land surface models is discussed. Received: 8 July 1999 / Accepted: 1 September 2000     

Comparing the Arctic climate in Chinese and other CMIP6 models

本研究采用来自耦合模式相互比较项目第六阶段(CMIP6)模式,评估和对比了10个中国模式和27个其他国际模式对北极冬季气候的历史模拟性能.本文的主要目的是展现中国模式对北极气候的模拟能力,并了解其在国际上的模拟水平.结果表明,对于气候态的模拟,中国模式在模拟北极温度场和大气场这些气候学方面与其他国际模式相当.而在趋势方面,中国模式同样和其他国际模式都能很好地模拟出北极变暖的特征.此外,与观测到的环流相比,CMIP6多模式集合平均值(MME)并没有显著的正趋势,这可能是因为外部强迫的作用.     

An ENSO stability analysis. Part II: results from the twentieth and twenty-first century simulations of the CMIP3 models

In this study, a Bjerknes stability (BJ) index, proposed by Jin et al. (2006), is adopted to assess the overall stability of El Niño and Southern Oscillation (ENSO) in state-of-the-art coupled models. The twentieth and twenty-first century simulations of 12 coupled models among the coupled model intercomparison project phase 3 models used in the intergovernmental panel on climate change forth assessment report demonstrate a significant positive correlation between ENSO amplitude and ENSO stability as measured by the BJ index. The simulations also show a diversity of behavior regarding the ENSO stability among the coupled models, which can be attributed to different mean state and sensitivity of an oceanic and atmospheric response to wind and SST forcing from model to model. When respective components of the BJ index obtained from the coupled models are compared with those from observations, it is revealed that most coupled models underestimate the thermodynamic damping effect and the positive effect of the zonal advective and thermocline feedback. Under increased CO₂ induced warm climate, changes, relative to the twentieth century simulations, in the damping and feedback terms responsible for the ENSO stability measured by the BJ index can be linked to mean state changes and associated atmospheric and oceanic response sensitivity changes. There is a clear multi-model trend in the damping terms and positive zonal advective feedback, thermocline feedback, and Ekman feedback terms under enhanced greenhouse gas conditions. However, the various behavior among the coupled models in competition between the positive feedback and negative damping terms in the BJ index formula prevent the formation of a definitive conclusion regarding future projections of ENSO stability using the current coupled models.     

Combining Monte Carlo and Ensemble Probabilities in Tropical Cyclone Forecasts near Landfall

The Monte Carlo probability(MCP) model, which has been used for official tropical cyclone(TC) warnings to the public by the United States' National Hurricane Center(NHC), can estimate the probability of wind speed in the vicinity of a TC during the forecast period. It has been successful in the operational environment for many years.However, due to its strong dependence on a given forecast track(e.g., forecast from the NCEP Global Forecast System), the MCP model may generate a poor probability map for TCs near landfall. In this study, we proposed and tested a modified MCP method for TC forecasts near landfall. We first adjusted the MCP model by adding limits to the direction angle and motion distance to deal with the substantial change in TC moving direction and the low wind speeds during landfall. Then, we combined ensemble probability maps generated from ECMWF, United Kingdom Met Office(UKMO), and NCEP ensemble forecasts, obtained from The International Grand Global Ensemble(TIGGE), into the MCP model to configure a modified MCP model. Wind speed probability maps for the 0–120-h forecast from both the original and modified MCP models are compared. It is found that the modified MCP model can provide a better wind speed probability map during landfall, especially at wind speeds of 20–64 kt near TC landfall. The results from this study prove the benefits of combining the MCP model with ensemble forecasting in potential applications for improved TC forecasts.     

Robustness of Recommended Farm Plans in England under Climate Change: A Monte Carlo Simulation

A methodology is described for estimating robustness of recommended farm plans under climate change while maintaining a meaningful representation of the underlying farm system. Monte Carlo Simulation (MCS) of crop yield data is used in conjunction with a fully specified farm-level model and output from a field worktime model. Estimates of farm net margin, enterprise mix (choice and area of enterprises), labour, machinery, storage and animal housing under mean crop yields and field worktimes for current (2000s) and 2050s conditions are generated. MCS is used to estimate the effect of crop yield variation on farm profitability and enterprise mix for the same periods by running the farm-level model with no constraints and running it constrained to the mean data plan. Estimates of robustness, measured as the percentage difference and the probability of exceeding the mean farm net-margin, were calculated from the outputs from these runs. For three representative farm types, mean farm net margin increased; however changes in robustness as shown by percentage difference in farm net margin depended on farm type while the probability of exceeding the mean plan net-margin decreased by 2050 indicating an increase in robustness. The most robust farm type had a diversified mix of enterprises and required no additional fixed resources by the 2050s. The least robust farm type was in a marginal location and mean plan recommendations for the 2050s required additional investment in fixed resources, particularly irrigation. It is concluded that the information provided by the methodology would be particularly useful to farmers: where mean data plans are not robust, MCS results could be used with financial planning techniques to minimise the impact of variability, rather than using high cost inputs to reduce variability per se.