Examensarbetet studerar möjligheterna att använda en statisk cross hedge för att prissäkra etanol. Situationen som analyseras är hämtad från Lantmännen Agroetanol. Agroetanol är Sveriges största producent av etanol och driver den första anläggning i Sverige där vete omvandlas till etanol. Anläggningen är Sveriges största och byggs för närvarande ut så att kapaciteten kommer under år 2008 kommer att öka med 300 procent. Priset på spannmål har stigit dramatiskt under år 2007 samtidigt som etanolpriset har sjunkit något. Mot bakgrund av dessa båda negativa prisrörelser utvärderas hedging med hjälp finansiella instrument som en möjlighet för Agroetanol att skydda sin produktion. Genom att använda futurekontrakt, med socker som underliggande tillgång, kan Agroetanol minska sin marknadsrisk. Efter en analys av Lantmännens befintliga riskmått i form av stresstest, konstateras att Lantmännen bör överväg att använda sig av Expected Shortfall för att mäta koncernens marknadsrisk. Expected Shortfall bygger på det mycket populära Value at Risk, men uppvisar ytterligare några fler positiva egenskaper. Vi rekommenderar att Lantmännenkoncernen använder sig av Expected Shortfall i arbetet med att kvantifiera sin finansiella marknadsrisk inom samtliga affärsområden och bolag. På detta sätt kan riskerna associerade med varje verksamhet enkelt analyseras. Slutligen kan den metodik för cross hedging som presenteras i examensarbetet användas i flera olika sammanhang och problemställningen är inte unik för groetanol. Författarna hoppas på detta sätt att undersökningen kan fungera som en vägledning även vid andra liknande projekt. / This master thesis studies the application of a static cross hedge when hedging ethanol. The case studied has been provided by Lantmännen Agroetanol, operator of the largest ethanol plant in Sweden. The plant produce ethanol from grain and the capacity is currently being expanded by 300 percent. Changes in the price of both grain and ethanol have been dramatic during 2007, with a decrease in the price of ethanol and a sharp increase in the price of wheat. These changes both have a negative impact on the operations of Agroetanol and this thesis look to hedging with futures as a method to lessen the exposure to price changes. Using future contracts derived on sugar prices we conclude that Agroetanol can decrease its market risk. An analysis of the methods for measuring financial risks at Lantmännen concludes that the use of Expected Shortfall, a measurement derived from Value at Risk, have a number of advantages. We therefore recommend that this measure is implemented throughout the corporation providing a consistent measure of financial risks. This enables every part of the organization to be analyzed based on its contribution to the total risk exposure. Finally the method used in the thesis can be used in a number of situations and the difficulties observed at Agroetanol are by no means unique. We hope that this study can provide an example for studies that aim to solve similar difficulties.

<p>Examensarbetet studerar möjligheterna att använda en statisk cross hedge för att prissäkra etanol. Situationen som analyseras är hämtad från Lantmännen Agroetanol. Agroetanol är Sveriges största producent av etanol och driver den första anläggning i Sverige där vete omvandlas till etanol. Anläggningen är Sveriges största och byggs för närvarande ut så att kapaciteten kommer under år 2008 kommer att öka med 300 procent. Priset på spannmål har stigit dramatiskt under år 2007 samtidigt som etanolpriset har sjunkit något. Mot bakgrund av dessa båda negativa prisrörelser utvärderas hedging med hjälp finansiella instrument som en möjlighet för Agroetanol att skydda sin produktion.</p><p>Genom att använda futurekontrakt, med socker som underliggande tillgång, kan Agroetanol minska sin marknadsrisk. Efter en analys av Lantmännens befintliga riskmått i form av stresstest, konstateras att Lantmännen bör överväg att använda sig av Expected Shortfall för att mäta koncernens marknadsrisk. Expected Shortfall bygger på det mycket populära Value at Risk, men uppvisar ytterligare några fler positiva egenskaper. Vi rekommenderar att Lantmännenkoncernen använder sig av Expected Shortfall i arbetet med att kvantifiera sin finansiella marknadsrisk inom samtliga affärsområden och bolag. På detta sätt kan riskerna</p><p>associerade med varje verksamhet enkelt analyseras. Slutligen kan den metodik för cross hedging som presenteras i examensarbetet användas i</p><p>flera olika sammanhang och problemställningen är inte unik för groetanol. Författarna hoppas på detta sätt att undersökningen kan fungera som en vägledning även vid andra liknande projekt.</p> / <p>This master thesis studies the application of a static cross hedge when hedging ethanol. The case studied has been provided by Lantmännen Agroetanol, operator of the largest ethanol plant in Sweden. The plant produce ethanol from grain and the capacity is currently being expanded by 300 percent. Changes in the price of both grain and ethanol have been dramatic during 2007, with a decrease in the price of ethanol and a sharp increase in the price of wheat. These changes both have a negative impact on the operations of Agroetanol and this thesis look to hedging with futures as a method to lessen the exposure to price changes.</p><p>Using future contracts derived on sugar prices we conclude that Agroetanol can decrease its market risk. An analysis of the methods for measuring financial risks at Lantmännen concludes that the use of Expected Shortfall, a measurement derived from Value at Risk, have a number of advantages. We therefore recommend that this measure is implemented throughout the corporation providing a consistent measure of financial risks. This enables every part of the organization to be analyzed based on its contribution to the total risk exposure.</p><p>Finally the method used in the thesis can be used in a number of situations and the difficulties observed at Agroetanol are by no means unique. We hope that this study can provide an example for studies that aim to solve similar difficulties.</p>

Some financial problems as minimizing the shortfall risk when hedging in incomplete markets lead to problems belonging to test theory. This paper considers a generalization of the Neyman-Pearson lemma. With methods of convex duality we deduce the structure of an optimal randomized test when testing a compound hypothesis against a simple alternative. We give necessary and sufficient optimality conditions for the problem.

Hedging has been one of the most important topics in finance. How to effectively hedge the exposed risk draws significant interest from both academicians and practitioners. In a complete financial market, every contingent claim can be hedged perfectly. In an incomplete market, the investor can eliminate his risk exposure by superhedging. However, both perfect hedging and superhedging usually call for a high cost. In some situations, the investor does not have enough capital or is not willing to spend that much to achieve a zero risk position. This brings us to the topic of partial hedging. In this thesis, we establish the risk measure based partial hedging model and study the optimal partial hedging strategies under various criteria. First, we consider two of the most common risk measures known as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). We derive the analytical forms of optimal partial hedging strategies under the criterion of minimizing VaR of the investor's total risk exposure. The knock-out call hedging strategy and the bull call spread hedging strategy are shown to be optimal among two admissible sets of hedging strategies. Since VaR risk measure has some undesired properties, we consider the CVaR risk measure and show that bull call spread hedging strategy is optimal under the criterion of minimizing CVaR of the investor's total risk exposure. The comparison between our proposed partial hedging strategies and some other partial hedging strategies, including the well-known quantile hedging strategy, is provided and the advantages of our proposed partial hedging strategies are highlighted. Then we apply the similar approaches in the context of reinsurance. The VaR-based optimal reinsurance strategies are derived under various constraints. Then we study the optimal partial hedging strategies under general risk measures. We provide the necessary and sufficient optimality conditions and use these conditions to study some specific hedging strategies. The robustness of our proposed CVaR-based optimal partial hedging strategy is also discussed in this part. Last but not least, we propose a new method, simulation-based approach, to formulate the optimal partial hedging models. By using the simulation-based approach, we can numerically obtain the optimal partial hedging strategy under various constraints and criteria. The numerical results in the examples in this part coincide with the theoretical results.

This thesis is focused on a theoretical explanation of some models for the optimization stock portfolios with different risk measure. The theory of the nonlinear programming is detailed developed and also basic Markowitz`s model with another optimization models as Konno -- Yamazaki`s model, Roy`s model, semivariance approach and Value at Risk approach, which are based on alternative risk measure. For all models the assumptions of their applications are highlighted and the comparation of these models is made too. Analytical part is concerned in the construction of the effecient portfolios according to the described models is made on the historical market prices of 13 companies traded on Prague Stock Exchange in SPAD.

This thesis deals with methods of stochastic programming and their application in financial investment. Theoretical part is devoted to basic terms of mathematical optimization, stochastic programming and decision making under uncertainty. Furter, there are introduced basic principles of modern portfolio theory, substantial part is devoted to risk measurement techniques in the context of investment, mostly to the methods Value at Risk and Expected shortfall. Practical part aims to creation of optimization models with an emphasis to minimize investment risk. Created models deal with real data and they are solved in optimization software GAMS.

Cette thèse développe des méthodes d'optimisation pour la gestion de la Supply Chain et a pour thème central la flexibilité définie comme la capacité à fournir un service ou un produit au consommateur dans un environnement incertain. La recherche a été menée dans le cadre d'un partenariat entre Argon Consulting, une société indépendante de conseil en Supply Chain et l'École des Ponts ParisTech. Dans cette thèse, nous développons trois sujets rencontrés par Argon Consulting et ses clients et qui correspondent à trois différents niveaux de décision (long terme, moyen terme et court terme).Lorsque les entreprises élargissent leur portefeuille de produits, elles doivent décider dans quelles usines produire chaque article. Il s'agit d'une décision à long terme, car une fois qu'elle est prise, elle ne peut être facilement modifiée. Plus qu'un problème d'affectation où un article est produit par une seule usine, ce problème consiste à décider si certains articles doivent être produits par plusieurs usines et par lesquelles. Cette interrogation est motivée par la grande incertitude de la demande. En effet, pour satisfaire la demande, l'affectation doit pouvoir équilibrer la charge de travail entre les usines. Nous appelons ce problème le multi-sourcing de la production. Comme il ne s'agit pas d'un problème récurrent, il est essentiel de tenir compte du risque au moment de décider le niveau de multi-sourcing. Nous proposons un modèle générique qui inclut les contraintes techniques du problème et une contrainte d'aversion au risque basée sur des mesures de risque issues de la théorie financière. Nous développons un algorithme et une heuristique basés sur les outils standards de la Recherche Opérationnelle et de l'Optimisation Stochastique pour résoudre le problème du multi-sourcing et nous testons leur efficacité sur des données réelles.Avant de planifier la production, certains indicateurs macroscopiques doivent être décidés à horizon moyen terme tels la quantité de matières premières à commander ou la taille des lots produits. Certaines entreprises utilisent des modèles de stock en temps continu, mais ces modèles reposent souvent sur un compromis entre les coûts de stock et les coûts de lancement. Ces derniers sont des coûts fixes payés au lancement de la production et sont difficiles à estimer en pratique. En revanche, à horizon moyen terme, la flexibilité des moyens de production est déjà fixée et les entreprises estiment facilement le nombre maximal de lancements. Poussés par cette observation, nous proposons des extensions de certains modèles classiques de stock en temps continu, sans coût de lancement et avec une limite sur le nombre d'installations. Nous avons utilisé les outils standard de l'Optimisation Continue pour calculer les indicateurs macroscopiques optimaux.Enfin, la planification de la production est une décision à court terme qui consiste à décider quels articles doivent être produits par la ligne de production pendant la période en cours. Ce problème appartient à la classe bien étudiée des problèmes de Lot-Sizing. Comme pour les décisions à moyen terme, ces problèmes reposent souvent sur un compromis entre les coûts de stock et les coûts de lancement. Fondant notre modèle sur ces considérations industrielles, nous gardons le même point de vue (aucun coût de lancement et une borne supérieure sur le nombre de lancement) et proposons un nouveau modèle.Bien qu'il s'agisse de décisions à court terme, les décisions de production doivent tenir compte de la demande future, qui demeure incertaine. Nous résolvons notre problème de planification de la production à l'aide d'outils standard de Recherche Opérationnelle et d'Optimisation Stochastique, nous testons l'efficacité sur des données réelles et nous la comparons aux heuristiques utilisées par les clients d'Argon Consulting / This thesis develops optimization methods for Supply Chain Management and is focused on the flexibility defined as the ability to deliver a service or a product to a costumer in an uncertain environment. The research was conducted throughout a partnership between Argon Consulting, which is an independent consulting firm in Supply Chain Operations and the École des Ponts ParisTech. In this thesis, we explore three topics that are encountered by Argon Consulting and its clients and that correspond to three different levels of decision (long-term, mid-term and short-term).When companies expand their product portfolio, they must decide in which plants to produce each item. This is a long-term decision since once it is decided, it cannot be easily changed. More than a assignment problem where one item is produced by a single plant, this problem consists in deciding if some items should be produced on several plants and by which plants. This is motivated by a highly uncertain demand. So, in order to satisfy the demand, the assignment must be able to balance the workload between plants. We call this problem the multi-sourcing of production. Since it is not a repeated problem, it is essential to take into account the risk when making the multi-sourcing decision. We propose a generic model that includes the technical constraints of the assignment and a risk-averse constraint based on risk measures from financial theory. We develop an algorithm and a heuristic based on standard tools from Operations Research and Stochastic Optimization to solve the multi-sourcing problem and we test their efficiency on real datasets.Before planning the production, some macroscopic indicators must be decided at mid-term level such as the quantity of raw materials to order or the size of produced lots. Continuous-time inventory models are used by some companies but these models often rely on a trade-off between holding costs and setups costs. These latters are fixed costs paid when production is launched and are hard to estimate in practice. On the other hand, at mid-term level, flexibility of the means of production is already fixed and companies easily estimate the maximal number of setups. Motivated by this observation, we propose extensions of some classical continuous-time inventory models with no setup costs and with a bound on the number of setups. We used standard tools from Continuous Optimization to compute the optimal macroscopic indicators.Finally, planning the production is a short-term decision consisting in deciding which items must be produced by the assembly line during the current period. This problem belongs to the well-studied class of Lot-Sizing Problems. As for mid-term decisions, these problems often rely on a trade-off between holding and setup costs. Basing our model on industrial considerations, we keep the same point of view (no setup cost and a bound on the number of setups) and propose a new model. Although these are short-term decisions, production decisions must take future demand into account, which remains uncertain. We solve our production planning problem using standard tools from Operations Research and Stochastic Optimization, test the efficiency on real datasets, and compare it to heuristics used by Argon Consulting's clients

The research on optimal reinsurance design dated back to the 1960’s. For nearly half a century, the quest for optimal reinsurance designs has remained a fascinating subject, drawing significant interests from both academicians and practitioners. Its fascination lies in its potential as an effective risk management tool for the insurers. There are many ways of formulating the optimal design of reinsurance, depending on the chosen objective and constraints. In this thesis, we address the problem of optimal reinsurance designs from an insurer’s perspective. For an insurer, an appropriate use of the reinsurance helps to reduce the adverse risk exposure and improve the overall viability of the underlying business. On the other hand, reinsurance incurs additional cost to the insurer in the form of reinsurance premium. This implies a classical risk and reward tradeoff faced by the insurer. The primary objective of the thesis is to develop theoretically sound and yet practical solution in the quest for optimal reinsurance designs. In order to achieve such an objective, this thesis is divided into two parts. In the first part, a number of reinsurance models are developed and their optimal reinsurance treaties are derived explicitly. This part focuses on the risk measure minimization reinsurance models and discusses the optimal reinsurance treaties by exploiting two of the most common risk measures known as the Value-at-Risk (VaR) and the Conditional Tail Expectation (CTE). Some additional important economic factors such as the reinsurance premium budget, the insurer’s profitability are also considered. The second part proposes an innovative method in formulating the reinsurance models, which we refer as the empirical approach since it exploits explicitly the insurer’s empirical loss data. The empirical approach has the advantage that it is practical and intuitively appealing. This approach is motivated by the difficulty that the reinsurance models are often infinite dimensional optimization problems and hence the explicit solutions are achievable only in some special cases. The empirical approach effectively reformulates the optimal reinsurance problem into a finite dimensional optimization problem. Furthermore, we demonstrate that the second-order conic programming can be used to obtain the optimal solutions for a wide range of reinsurance models formulated by the empirical approach.

The research on optimal reinsurance design dated back to the 1960’s. For nearly half a century, the quest for optimal reinsurance designs has remained a fascinating subject, drawing significant interests from both academicians and practitioners. Its fascination lies in its potential as an effective risk management tool for the insurers. There are many ways of formulating the optimal design of reinsurance, depending on the chosen objective and constraints. In this thesis, we address the problem of optimal reinsurance designs from an insurer’s perspective. For an insurer, an appropriate use of the reinsurance helps to reduce the adverse risk exposure and improve the overall viability of the underlying business. On the other hand, reinsurance incurs additional cost to the insurer in the form of reinsurance premium. This implies a classical risk and reward tradeoff faced by the insurer. The primary objective of the thesis is to develop theoretically sound and yet practical solution in the quest for optimal reinsurance designs. In order to achieve such an objective, this thesis is divided into two parts. In the first part, a number of reinsurance models are developed and their optimal reinsurance treaties are derived explicitly. This part focuses on the risk measure minimization reinsurance models and discusses the optimal reinsurance treaties by exploiting two of the most common risk measures known as the Value-at-Risk (VaR) and the Conditional Tail Expectation (CTE). Some additional important economic factors such as the reinsurance premium budget, the insurer’s profitability are also considered. The second part proposes an innovative method in formulating the reinsurance models, which we refer as the empirical approach since it exploits explicitly the insurer’s empirical loss data. The empirical approach has the advantage that it is practical and intuitively appealing. This approach is motivated by the difficulty that the reinsurance models are often infinite dimensional optimization problems and hence the explicit solutions are achievable only in some special cases. The empirical approach effectively reformulates the optimal reinsurance problem into a finite dimensional optimization problem. Furthermore, we demonstrate that the second-order conic programming can be used to obtain the optimal solutions for a wide range of reinsurance models formulated by the empirical approach.

In this thesis the performances of different approximations are compared for a standard actuarial and financial problem: the estimation of quantiles and conditional tail expectations of the final value of a series of discrete cash flows. To calculate the risk measures such as quantiles and Conditional Tail Expectations, one needs the distribution function of the final wealth. The final value of a series of discrete payments in the considered model is the sum of dependent lognormal random variables. Unfortunately, its distribution function cannot be determined analytically. Thus usually one has to use time-consuming Monte Carlo simulations. Computational time still remains a serious drawback of Monte Carlo simulations, thus several analytical techniques for approximating the distribution function of final wealth are proposed in the frame of this thesis. These are the widely used moment-matching approximations and innovative comonotonic approximations. Moment-matching methods approximate the unknown distribution function by a given one in such a way that some characteristics (in the present case the first two moments) coincide. The ideas of two well-known approximations are described briefly. Analytical formulas for valuing quantiles and Conditional Tail Expectations are derived for both approximations. Recently, a large group of scientists from Catholic University Leuven in Belgium has derived comonotonic upper and comonotonic lower bounds for sums of dependent lognormal random variables. These bounds are bounds in the terms of "convex order". In order to provide the theoretical background for comonotonic approximations several fundamental ordering concepts such as stochastic dominance, stop-loss and convex order and some important relations between them are introduced. The last two concepts are closely related. Both stochastic orders express which of two random variables is the "less dangerous/more attractive" one. The central idea of comonotonic upper bound approximation is to replace the original sum, presenting final wealth, by a new sum, for which the components have the same marginal distributions as the components in the original sum, but with "more dangerous/less attractive" dependence structure. The upper bound, or saying mathematically, convex largest sum is obtained when the components of the sum are the components of comonotonic random vector. Therefore, fundamental concepts of comonotonicity theory which are important for the derivation of convex bounds are introduced. The most wide-spread examples of comonotonicity which emerge in financial context are described. In addition to the upper bound a lower bound can be derived as well. This provides one with a measure of the reliability of the upper bound. The lower bound approach is based on the technique of conditioning. It is obtained by applying Jensen's inequality for conditional expectations to the original sum of dependent random variables. Two slightly different version of conditioning random variable are considered in the context of this thesis. They give rise to two different approaches which are referred to as comonotonic lower bound and comonotonic "maximal variance" lower bound approaches. Special attention is given to the class of distortion risk measures. It is shown that the quantile risk measure as well as Conditional Tail Expectation (under some additional conditions) belong to this class. It is proved that both risk measures being under consideration are additive for a sum of comonotonic random variables, i.e. quantile and Conditional Tail Expectation for a comonotonic upper and lower bounds can easily be obtained by summing the corresponding risk measures of the marginals involved. A special subclass of distortion risk measures which is referred to as class of concave distortion risk measures is also under consideration. It is shown that quantile risk measure is not a concave distortion risk measure while Conditional Tail Expectation (under some additional conditions) is a concave distortion risk measure. A theoretical justification for the fact that "concave" Conditional Tail Expectation preserves convex order relation between random variables is given. It is shown that this property does not necessarily hold for the quantile risk measure, as it is not a concave risk measure. Finally, the accuracy and efficiency of two moment-matching, comonotonic upper bound, comonotonic lower bound and "maximal variance" lower bound approximations are examined for a wide range of parameters by comparing with the results obtained by Monte Carlo simulation. It is justified by numerical results that, generally, in the current situation lower bound approach outperforms other methods. Moreover, the preservation of convex order relation between the convex bounds for the final wealth by Conditional Tail Expectation is demonstrated by numerical results. It is justified numerically that this property does not necessarily hold true for the quantile.