Fuzzy risk adjusted performance measures: Application to hedge funds

In this paper, following the notion of probabilistic risk adjusted performance measures, we introduce that of fuzzy risk adjusted performance measures (FRAPM). In order to deal efficiently with the closing-based returns bias induced by market microstructure noise, as well as to handle their uncertain variability, we combine fuzzy set theory and probability theory. The returns are first represented as fuzzy random variables and then used in defining fuzzy versions of some adjusted performance measures. Using a recent ordering method for fuzzy numbers, we propose a ranking of funds based on these fuzzy performance measures. Finally, empirical studies carried out on fifty French hedge funds confirm the effectiveness and give the benefits of our approach over the classical performance ratios.     

The forgotten sons: Warehousing systems for brick-and-mortar retail chains

Warehouses are an inevitable component in any supply chain and a vividly investigated object of research. Much attention, however, is absorbed by warehousing systems dedicated to the special needs of online retailers in the business-to-consumer segment. Due to the ever increasing sales volumes of e-commerce this focus seems self-evident, but a much larger fraction of retail sales are still realized by traditional brick-and-mortar stores. The special needs of warehouses servicing these stores are focused in this paper. While e-commerce warehouses face low-volume-high-mix picking orders, because private households tend to order just a few pieces per order from a large assortment, distribution centers of retail chains rather have to process high-volume-low-mix orders. We elaborate the basic requirements within both business segments and identify suited warehousing systems for brick-and-mortar stores (e.g., fully-automated case picking). The setup of each identified warehousing system is described, elementary decision problems are discussed, and the existing literature is surveyed. Furthermore, we identify future research needs.     

基于EPU指数的我国寿险市场需求影响因素分析

近年来我国寿险市场发展迅速,已成为全球第二大寿险市场.自2008年金融危机以来国际国内均对经济政策EPU指数施以更多关注.从定性和定量两个角度分析EPU指数对我国寿险市场需求的影响,运用向量自回归模型实证分析EPU指数对寿险市场需求的影响程度,基于实证分析结论为寿险市场健康发展提出相应的政策建议.     

Extraction of characteristic points and its fractal reconstruction for terrain profile data

The main objective of this paper is to study reduction rate of 2D DEM (digital elevation model) data profile after data reduction by the Douglas–Peucker (DP) linear simplification method and by fractal interpolation to show original terrain reconstruction. In this paper, two-dimensional data of measured geographic profiles are taken as the study object, by using the DP method and the improved Douglas–Peucker (IDP) method to reduce data. Its aim is to retain spatial linear characteristics and variations, then take reduced data points as basic points and use the random fractal interpolation approach to add more data points up to the same as the original data points, in order to reconstruct the terrain, and compare the experimental data with the random point extraction method addressed in related literature. This paper uses tolerance calibration to generate different reduction rates and utilizes four types of evaluation factors, statistical measurement, image measurement, spectral analysis and elevation cumulative probability distribution graph, to make a quantitative analysis of profile variation. The study result indicates that real profile elevation data, manipulated with varied reduction approaches, then reconstructed by means of fractal interpolation can produce data points with a higher resolution than those originally observed, thereby the reconstructed profile gets more natural and real details.     

Mean-field type forward-backward doubly stochastic differential equations and related stochastic differential games

We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations, in which the coefficient contains not only the state process but also its marginal distribution, and the cost functional is also of mean-field type. It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motions. We establish a necessary condition in the form of maximum principle and a verification theorem, which is a sufficient condition for Nash equilibrium point. We use the theoretical results to deal with a partial information linear-quadratic (LQ) game, and obtain the unique Nash equilibrium point for our LQ game problem by virtue of the unique solvability of mean-field forward-backward doubly stochastic differential equation.     

Price dynamics in the European Union Emissions Trading System and evaluation of its ability to boost emission-related investment decisions

The price of permits in the European Union Emissions Trading System (EU ETS) has historically been highly sensitive and prone to jumps. We consider different stochastic processes to model the price of permits, and show that the Variance Gamma (VG) model provides the best fit for the price distribution, among a selection of infinite activity processes. Using this result as a starting point, we assess the effects of the EU ETS in delivering low-carbon investments at the firm level, by modeling a price taker electricity producer subject to the EU ETS jurisdiction. We compute, via Least Squares Monte Carlo, the value of the real option the greenhouse gas emitter has, consisting in the opportunity to switch from its current high-carbon technology to a cleaner one. We use a VG specification for carbon prices, and a mean-reverting (Brennan–Schwartz) process for the price of fuel. Moreover, we further analyze the investment decision problem, in case of a CO₂ price stabilization mechanism in the form of a price floor, by explicitly computing the expected value of the investment project by means of Fourier methods. Our results show that the introduction of the price stabilization mechanism significantly affects the timing of the investment decision, and supports emission-related investments.     

Controlling distribution inventory systems with shipment consolidation and compound Poisson demand

We consider a one-warehouse-multiple-retailer inventory system where the retailers face stochastic customer demand, modelled as compound Poisson processes. Deliveries from the central warehouse to groups of retailers are consolidated using a time based shipment consolidation policy. This means that replenishment orders have to wait until a vehicle departures, which increases the lead time for the retailers and therefore also the safety stock. Thus, a trade-off exists between expected shipment costs and holding costs. Our aim is to determine the shipment intervals and the required amount of safety stock for each retailer and the warehouse to minimize total cost, both for backorder costs and fill rate constraints. Previous work has focused on exact solutions which are computationally demanding and not applicable for larger real world problems. The focus of our present work is on the development of computationally attractive heuristics that can be applied in practice. A numerical study shows that the proposed heuristics perform well compared to the exact cost minimizing solutions. We also illustrate that the approaches are appropriate for solving real world problems using data from a large European company.     

平均场倒向重随机微分方程及其应用

研究了平均场倒向随重机微分方程, 得到了平均场倒向重随机微分方程解的存在唯一性.基于平均场倒向重随机微分方程的解, 给出了一类非局部随机偏微分方程解的概率解释.讨论了平均场倒向重随机系统的最优控制问题, 建立了庞特利亚金型的最大值原理.最后讨论了一个平均场倒向重随机线性二次最优控制问题, 展示了上述最大值原理的应用.     

Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility

We consider the pricing of long-dated insurance contracts under stochastic interest rates and stochastic volatility. In particular, we focus on the valuation of insurance options with long-term equity or foreign exchange exposures. Our modeling framework extends the stochastic volatility model of Schöbel and Zhu (1999) by including stochastic interest rates. Moreover, we allow all driving model factors to be instantaneously correlated with each other, i.e. we allow for a general correlation structure between the instantaneous interest rates, the volatilities and the underlying stock returns. As insurance products often incorporate long-term exposures, they are typically more sensitive to changes in the interest rates, volatility and currencies. Therefore, having the flexibility to correlate the underlying asset price with both the stochastic volatility and the stochastic interest rates, yields a realistic model which is of practical importance for the pricing and hedging of such long-term contracts. We show that European options, typically used for the calibration of the model to market prices, and forward starting options can be priced efficiently and in closed-form by means of Fourier inversion techniques. We extensively discuss the numerical implementation of these pricing formulas, allowing for a fast and accurate valuation of European and forward starting options. The model will be especially useful for the pricing and risk management of insurance contracts and other exotic derivatives involving long-term maturities.     

Dual models of interval DEA and its extension to interval data

The purpose of this paper is to develop a new DEA with an interval efficiency. An original DEA model is to evaluate each DMU optimistically. There is another model called “Inverted DEA” to evaluate each DMU pessimistically. But, there are no relations essentially between DEA and inverted DEA. Thus, we formulate a DEA model with an interval efficiency which consists of efficiencies obtained from the optimistic and pessimistic viewpoints. Thus, two end points can construct an interval efficiency. With the same idea, we deal with the interval inefficiency model which is inverse to interval efficiency. Finally, we extend the proposed DEA model to interval data and fuzzy data.