Recent applications of theory of the firm under uncertainty

This paper provides a comprehensive synthesis and analysis of the current and recent empirical implementations of the theory of the firm under uncertainty, including multiple sources of uncertainty. In so doing, it identifies the major estimation obstacles and it offers the future empirical researcher ways to derive simple estimation procedures under multiple sources uncertainty.     

Conditional VaR estimation using Pearson’s type IV distribution

This paper presents a new value at risk (VaR) estimation model for equity returns time series and tests it extensively on Stock Indices of 14 countries. Two most important stylized facts of such series are volatility clustering, and non-normality as a result of fat tails of the return distribution. While volatility clustering has been extensively studied using the GARCH model and its various extensions, the phenomenon of non-normality has not been comprehensively explored, at least in the context of VaR estimation. A combination of extreme value theory (EVT) and GARCH has been explored to analyze financial data showing non-normal behavior. This paper proposes a combination of the Pearson’s Type IV distribution and the GARCH (1, 1) approach to furnish a new method with superior predictive abilities. The approach is back tested for the entire sample as well as for a holdout sample using rolling windows.     

Parameter uncertainty, sensitivity analysis and prediction error in a water-balance hydrological model

Analysis of uncertainty is often neglected in the evaluation of complex systems models, such as computational models used in hydrology or ecology. Prediction uncertainty arises from a variety of sources, such as input error, calibration accuracy, parameter sensitivity and parameter uncertainty. In this study, various computational approaches were investigated for analysing the impact of parameter uncertainty on predictions of streamflow for a water-balance hydrological model used in eastern Australia. The parameters and associated equations which had greatest impact on model output were determined by combining differential error analysis and Monte Carlo simulation with stochastic and deterministic sensitivity analysis. This integrated approach aids in the identification of insignificant or redundant parameters and provides support for further simplifications in the mathematical structure underlying the model. Parameter uncertainty was represented by a probability distribution and simulation experiments revealed that the shape (skewness) of the distribution had a significant effect on model output uncertainty. More specifically, increasing negative skewness of the parameter distribution correlated with decreasing width of the model output confidence interval (i.e. resulting in less uncertainty). For skewed distributions, characterisation of uncertainty is more accurate using the confidence interval from the cumulative distribution rather than using variance. The analytic approach also identified the key parameters and the non-linear flux equation most influential in affecting model output uncertainty.     

Wireless network capacity management: A real options approach

This paper applies financial option valuation methods to new wireless network capacity investment decision timing. In particular, we consider the case of network capacity for cellular telephone service. Given a cluster of base stations (with a certain traffic capacity per base station), we determine when it is optimal to increase capacity for each of the base stations contained in the cluster. We express this in terms of the fraction of total cluster capacity in use, i.e. we calculate the optimal time to upgrade in terms of the ratio of observed usage to existing capacity. We study the optimal decision problem of adding new capacity in the presence of stochastic wireless demand for services. A four factor algorithm is developed, based on a real options formulation. Numerical examples are provided to illustrate various aspects of the model.     

A stochastic model for risk management in global supply chain networks

With the increasing emphasis on supply chain vulnerabilities, effective mathematical tools for analyzing and understanding appropriate supply chain risk management are now attracting much attention. This paper presents a stochastic model of the multi-stage global supply chain network problem, incorporating a set of related risks, namely, supply, demand, exchange, and disruption. We provide a new solution methodology using the Moreau–Yosida regularization, and design an algorithm for treating the multi-stage global supply chain network problem with profit maximization and risk minimization objectives.     

保单个数为Poisson分布的总理赔额分布函数的界值研究

根据单个保单理赔额分布函数F(z)的一些特殊性质,研究了开放个别风险模型在保单个数N为Poisson分布下,总理赔额分布函数F_S(x)对任意x(x≥0)的界值问题,得到一些实用的、便于数值计算的界值结果,具有重要的应用价值．     

保险联结风险投资模型的赤字问题

保险公司被允许将部分资金投入风险市场,这样保险公司经营的风险来自于未来实际发生索赔的不确定性和投资收益的不确定性。研究了由经典的Cramer-Lundberg模型与按照几何布朗运动股票价格变动的一个风险模型,获得了三种资产分配情况下股票价格波动对赤字发生概率下界的影响。     

Variable Fuzzy Sets and its Application in Comprehensive Risk Evaluation for Flood-control Engineering System

Due to significance of the engineering system for flood control and the multi-dimensional synthesis of the risk evaluation issue that the paper selects typical risk indexes to classify risk degree of flood-control engineering. Under global view of system that the variable fuzzy sets method is presented to set up comprehensive evaluation model for flood-control engineering system (FCES). The method can scientifically and reasonably determine membership degrees and relative membership functions of disquisitive indexes at level interval that relating to engineering, also it can fully use one’s experience and knowledge, qualitative and quantitative information of index system to obtain weights of indexes for operating comprehensive risk evaluation for FCES. The numerical example shows that the proposed method is feasible and effective, and the evaluation results are reasonable.     

Distributionally robust modeling of optimal control

The aim of this paper is to formulate several questions related to distributionally robust Stochastic Optimal Control modeling. As an example the distributionally robust counterpart of the classical inventory model is discussed in details. Finite and infinite horizon stationary settings are considered.     

应用复合极值理论计算VaR1

本文介绍了一种复合极值理论,并将其应用到VaR的计算上。实际中大的损失发生的频率也是风险的一种度量,在应用复合极值理论方法计算VaR时,我们第一次将在一定时期内金融资产的损失率超过一定阈值的次数的分布和收益率的分布结合了起来,对欧元/人民币、日元/人民币两种汇率进行了VaR的计算,经过实证分析,得到了一些有意义的结果。