Interval LU-fuzzy arithmetic in the Black and Scholes option pricing

In financial markets people have to cope with a lot of uncertainty while making decisions. Many models have been introduced in the last years to handle vagueness but it is very difficult to capture together all the fundamental characteristics of real markets. Fuzzy modeling for finance seems to have some challenging features describing the financial markets behavior; in this paper we show that the vagueness induced by the fuzzy mathematics can be relevant in modelling objects in finance, especially when a flexible parametrization is adopted to represent the fuzzy numbers. Fuzzy calculus for financial applications requires a big amount of computations and the LU-fuzzy representation produces good results due to the fact that it is computationally fast and it reproduces the essential quality of the shape of fuzzy numbers involved in computations. The paper considers the Black and Scholes option pricing formula, as long as many other have done in the last few years. We suggest the use of the LU-fuzzy parametric representation for fuzzy numbers, introduced in Guerra and Stefanini and improved in Stefanini, Sorini and Guerra, in the framework of the Black and Scholes model for option pricing, everywhere recognized as a benchmark; the details of the computations by the interval fuzzy arithmetic approach and an illustrative example are also incuded.Fuzzy Operations, Option Pricing, Black and Scholes

Fuzzy Optimization of Option Pricing Model and Its Application in Land Expropriation

Option pricing is irreversible, fuzzy, and flexible. The fuzzy measure which is used for real option pricing is a useful supplement to the traditional real option pricing method. Based on the review of the concepts of the mean and variance of trapezoidal fuzzy number and the combination with the Carlsson-Fuller model, the trapezoidal fuzzy variable can be used to represent the current price of land expropriation and the sale price of land on the option day. Fuzzy Black-Scholes option pricing model can be constructed under fuzzy environment and problems also can be solved and discussed through numerical examples

Sustainable supply chain network design integrating logistics outsourcing decisions in the context of uncertainties

Les fournisseurs de services logistiques (3PLs) possèdent des potentialités pour activer les pratiques de développement durables entre les différents partenaires d’une chaîne logistique (Supply Chain SC). Il existe un niveau optimal d'intégration des 3PLs en tant que fournisseurs, pour s’attendre à des performances opérationnelles élevées au sein de toute la SC. Ce niveau se traduit par la distinction des activités logistiques à externaliser de celles à effectuer en interne. Une fois que les activités logistiques externalisés sont stratégiquement identifiées, et tactiquement dimensionnées, elles doivent être effectuées par des 3PLs appropriés afin d’endurer les performances économiques ; sociales ; et environnementales de la SC. La présente thèse développe une approche holistique pour concevoir une SC durable intégrant les 3PLs, dans un contexte incertain d’affaires et politique de carbone. Premièrement, une approche de modélisation stochastique en deux étapes est suggérée pour optimiser à la fois le niveau d'intégration des 3PLs, et le niveau d'investissement en technologies sobres au carbone, et ce dans le contexte d’une SC résiliente aux changements climatiques. Notre SC est structurée de façon à capturer trois principales préoccupations du Supply Chain Management d’une entreprise focale FC (e. g. le fabricant) : Sécurité d’approvisionnement, Segmentation de distribution, et Responsabilité élargie des producteurs. La première étape de l'approche de modélisation suggère un plan stochastique basé sur des scenarios plus probables, afin de capturer les incertitudes inhérentes à tout environnement d’affaires (e. g. la fluctuation de la demande des différents produits ; la qualité et la quantité de retour des produits déjà utilisés ; et l’évolution des différents coûts logistiques en fonction du temps). Puis, elle propose un modèle de programmation stochastique bi-objectif, multi-période, et multi-produit. Le modèle de programmation quadratique, et non linéaire consiste à minimiser simultanément le coût logistique total espéré, et les émissions de Gaz à effet de Serre de la SC fermée. L'exécution du modèle au moyen d'un algorithme basé sur la méthode Epsilon-contraint conduit à un ensemble de configurations Pareto optimales d’une SC dé- carbonisée, avant tout investissement en technologie sobre au carbone. Chacune de ces configurations sépare les activités logistiques à externaliser de celles à effectuer en interne. La deuxième étape de l'approche de modélisation permet aux décideurs de choisir la meilleure configuration de la SC parmi les configurations Pareto optimales identifiées. Le concept de Prix du Carbone Interne est utilisé pour établir un plan stochastique du prix de carbone, dans le cadre d'un régime de déclaration volontaire du carbone. Nous proposons un ensemble des technologies sobres au carbone, dans le domaine de transport des marchandises, disposées à concourir pour contrer les politiques incertaines de carbone. Un modèle stochastique combinatoire, et linéaire est développé pour minimiser le coût total espéré, sous contraintes de l’abattement du carbone; limitation du budget, et la priorité attribuée pour chaque Technologie Réductrice de carbone (Low Carbone Reduction LCR). L'injection de chaque solution Pareto dans le modèle, et la résolution du modèle conduisent à sélectionner la configuration de la SC, la plus résiliente aux changements climatiques. Cette configuration définit non seulement le plan d'investissement optimal en LCR, mais aussi le niveau optimal d’externalisation de la logistique dans la SC. Deuxièmement, une fois que les activités logistiques à externaliser sont stratégiquement définies et tactiquement dimensionnées, elles ont besoin d’être effectuées par des 3PL appropriées, afin de soutenir la FC à construire une SC durable et résiliente. Nous suggérons DEA-QFD / Fuzzy AHP- Conception robuste de Taguchi : Une approche intégrée & robuste, pour sélectionner les 3PL candidats les plus efficients. Les critères durables et les risques liés à l’environnement d’affaires, sont identifiés, classés et ordonnés. Le Déploiement de la Fonction Qualité (QFD) est renforcé par le Processus Hiérarchique Analytique (AHP), et par la logique floue pour déterminer avec consistance l'importance relative de chaque facteur de décision, et ce, conformément aux besoins logistiques réels, et stratégies d'affaires de la FC. L’Analyse d’Enveloppement des Données (DEA) Data Envelopment Analysis conduit à limiter la liste des candidats, uniquement à ceux d’efficiences comparables, et donc excluant tout candidat moins efficient. La technique de conception robuste Taguchi permet de réaliser un plan d'expérience qui détermine un candidat idéal nommé 'optimum de Taguchi' ; un Benchmark pour comparer les 3PLs candidats. Par suite, le 3PL le plus efficient est celui le plus proche de cet optimum. Nous conduisons actuellement une étude de cas d’une entreprise qui fabrique et commercialise les fours à micro-ondes pour valider la modélisation stochastique en deux étapes. Certains aspects concernant l’application de l’approche sont reportés. Enfin, un exemple de sélection d’un 3PL durable pour s’occuper de la logistique inverse est fourni, pour démontrer l'applicabilité de l'approche intégrée & robuste, et montrer sa puissance par rapport aux approches populaires de sélection.The Third-Party Logistics service providers (3PLs) have the potentialities to activate sustainable practices between different partners of a Supply Chain (SC). There exists an optimal level of integrating 3PLs as suppliers of a Focal Company within the SC, to expect for high operational performances. This level leads to distinguish all the logistics activities to outsource from those to perform in-house. Once the outsourced logistics activities are strategically identified, and tactically dimensioned, they need to be performed by appropriate 3PLs to sustain economic, social and environmental performances of the SC. The present thesis develops a holistic approach to design a sustainable supply chain integrating 3PLs, in the context of business and carbon policy uncertainties. First, a two-stage stochastic modelling approach is suggested to optimize both the level of 3PL integration, and of Low Carbon Reduction LCR investment within a climate change resilient SC. Our SC is structured to capture three main SC management issues of the Focal Company FC (e.g. The manufacturer) : Security of Supplies; Distribution Segmentation; and Extended Producer Responsibility. The first-stage of the modelling approach suggests a stochastic plan based scenarios capturing business uncertainties, and proposes a two-objective, multi-period, and multi-product programming model, for minimizing simultaneously, the expected logistics total cost, and the Green House Gas GHG emissions of the whole SC. The run of the model by means of a suggested Epsilon-constraint algorithm leads to a set of Pareto optimal decarbonized SC configurations, before any LCR investment. Each one of these configurations distinguishes the logistics activities to be outsourced, from those to be performed in-house. The second-stage of the modelling approach helps the decision makers to select the best Pareto optimal SC configuration. The concept of internal carbon price is used to establish a stochastic plan of carbon price in the context of a voluntary carbon disclosure regime, and we propose a set of LCR technologies in the freight transportation domain ready to compete for counteracting the uncertain carbon policies. A combinatory model is developed to minimize the total expected cost, under the constraints of; carbon abatement, budget limitation, and LCR investment priorities. The injection of each Pareto optimal solution in the model, and the resolution lead to select the most efficient climate resilient SC configuration, which defines not only the optimal plan of LCR investment, but the optimal level of logistics outsourcing within the SC as well. Secondly, once the outsourced logistics are strategically defined they need to be performed by appropriate 3PLs for supporting the FC to build a Sustainable SC. We suggest the DEA-QFD/Fuzzy AHP-Taguchi Robust Design: a robust integrated selection approach to select the most efficient 3PL candidates. Sustainable criteria, and risks related to business environment are identified, categorized, and ordered. Quality Function Deployment (QFD) is reinforced by Analytic Hierarchic Process (AHP), and Fuzzy logic, to consistently determine the relative importance of each decision factor according to the real logistics needs, and business strategies of the FC. Data Envelopment Analysis leads to shorten the list of candidates to only those of comparative efficiencies. The Taguchi Robust Design technique allows to perform a plan of experiment, for determining an ideal candidate named ‘optimum of Taguchi’. This benchmark is used to compare the remainder 3Pls candidates, and the most efficient 3PL is the closest one to this optimum.We are currently conducting a case study of a company that manufactures and markets microwave ovens for validating the two-stage stochastic approach, and certain aspects of its implementation are provided. Finally, an example of selecting a sustainable 3PL, to handle reverse logistics is given for demonstrating the applicability of the integrated & robust approach, and showing its power compared to popular selection approaches. Keywords:Third Party Logistics; Green Supply Chain design; Stochastic Multi-Objective Optimization; Carbon Pricing; Taguchi Robust Design

Applications of Fuzzy Set Theory, Fuzzy Measure Theory and Fuzzy Differential Calculus

This research tackles the issue of uncertainty due to lack of information, alternatively known as Knightian Uncertainty, and its impact on option pricing. In the presence of such uncertainty, Probability Theory becomes restrictive and alternative tools are called for. In this research, we consider tools of Fuzzy Theory. We introduce three Option Pricing Models the first of which is a fuzzy binomial model based on the standard CRR binomial model. The model performs option pricing in a fuzzy world characterized by blurred prices. In such a world, it is no longer possible to price by replication. So we introduce a fuzzy pricing approach that employs Sugeno integration and fuzzy measures, and generates bounds on the possible option price. The second model is a fuzzy Black-Scholes model, which prices options in the presence of uncertain or fuzzy volatility. We model such volatility by establishing bounds on the corresponding fuzzy values thereby generating fuzzy bounds on the possible option price. Finally, the third model is an extension on an existing one period fuzzy binomial model that prices options when the underlying price is characterized by opacity. The option price returned by this model is dependent on a market parameter that summarizes its completeness. However, it is possible to defuzzify the last two models to obtain one crisp price that summarizes market information. The last two models outperform their standard counterparts

A Network Model of Financial Markets

This thesis introduces a network representation of equity markets.The model is based on the premise that assets share dependencies on abstract ‘factors’ resulting in exploitable patterns among asset price levels.The network model is a collection of long-run market trends estimated by a 3 layer machine learning framework.The network model’s comprehensive validity is established with 2 simulations in the fields of algorithmic trading, and systemic risk.The algorithmic trading validation applies expectations derived from the network model to estimating expected future returns. It further utilizes the network’s expectations to actively manage a theoretically market neutral portfolio.The validation demonstrates that the network model’s portfolio generates excess returns relative to 2 benchmarks. Over the time period of April, 2007 to January, 2014 the network model’s portfolio for assets drawn from the S&P/ASX 100 produced a Sharpe ratio of 0.674.This approximately doubles the nearest benchmark. The systemic risk validation utilized the network model to simulate shocks to select market sectors and evaluate the resulting financial contagion.The validation successfully differentiated sectors by systemic connectivity levels and suggested some interesting market features. Most notable was the identification of the ‘Financials’ sector as most systemically influential and ‘Basic Materials’ as the most systemically dependent. Additionally, there was evidence that ‘Financials’ may function as a hub of systemic risk which exacerbates losses from multiple market sectors

Self-adaptation via concurrent multi-action evaluation for unknown context

Context-aware computing has been attracting growing attention in recent years. Generally, there are several ways for a context-aware system to select a course of action for a particular change of context. One way is for the system developers to encompass all possible context changes in the domain knowledge. Other methods include system inferences and adaptive learning whereby the system executes one action and evaluates the outcome and self-adapts/self-learns based on that. However, in situations where a system encounters unknown contexts, the iterative approach would become unfeasible when the size of the action space increases. Providing efficient solutions to this problem has been the main goal of this research project. Based on the developed abstract model, the designed methodology replaces the single action implementation and evaluation by multiple actions implemented and evaluated concurrently. This parallel evaluation of actions speeds up significantly the evolution time taken to select the best action suited to unknown context compared to the iterative approach. The designed and implemented framework efficiently carries out concurrent multi-action evaluation when an unknown context is encountered and finds the best course of action. Two concrete implementations of the framework were carried out demonstrating the usability and adaptability of the framework across multiple domains. The first implementation was in the domain of database performance tuning. The concrete implementation of the framework demonstrated the ability of concurrent multi-action evaluation technique to performance tune a database when performance is regressed for an unknown reason. The second implementation demonstrated the ability of the framework to correctly determine the threshold price to be used in a name-your-own-price channel when an unknown context is encountered. In conclusion the research introduced a new paradigm of a self-adaptation technique for context-aware application. Among the existing body of work, the concurrent multi-action evaluation is classified under the abstract concept of experiment-based self-adaptation techniques

Quantum Machine Learning: A Patent Review

One of the central problems bottlenecking machine learning research is classical computational power limits. Quantum computing provides a solution, offering more processing power for less electric cost. Quantum Machine Learning (QML) is a research field at the intersection of quantum computing and machine learning technologies, driving the cutting edge in technological innovation. While the legal literature on software patents is rapidly scaling, the research focused on QML patents is noticeably nascent. As such, this Article contributes the first empirical patent survey for QML technologies