Programme in Advanced Mathematics of Finance, University of the Witwatersrand, Johannesburg. / Peng introduced a typical ltration consistent nonlinear expectation, called a g-expectation in [40]. It satis es all properties of the classical mathematical expectation besides the linearity. Peng's conditional g-expectation is a solution to a backward stochastic di erential equation (BSDE) within the classical framework of It^o's calculus, with terminal condition given at some xed time T. In addition, this g-expectation is uniquely speci ed by a real function g satisfying certain properties. Many properties of the g-expectation, which will be presented, follow from the speci cation of this function. Martingales, super- and submartingales have been de ned in the nonlinear setting of g-expectations. Consequently, a nonlinear Doob-Meyer decomposition theorem was proved. Applications of g-expectations in the mathematical nancial world have also been of great interest. g-Expectations have been applied to the pricing of contingent claims in the nancial market, as well as to risk measures. Risk measures were introduced to quantify the riskiness of any nancial position. They also give an indication as to which positions carry an acceptable amount of risk and which positions do not. Coherent risk measures and convex risk measures will be examined. These risk measures were extended into a nonlinear setting using the g-expectation. In many cases due to intermediate cash ows, we want to work with a multi-period, dynamic risk measure. Conditional g-expectations were then used to extend dynamic risk measures into the nonlinear setting. The Choquet expectation, introduced by Gustave Choquet, is another nonlinear expectation. An interesting question which is examined, is whether there are incidences when the g-expectation and the Choquet expectation coincide.

M.Sc. (Statistics) / Most people in the world rely on a well-functioning and stable financial system. Problems experienced by financial institutions, such as too little liquidity or large amounts of bad debt, can easily influence companies and individuals, creating a chain reaction comparable to an avalanche. Financial institutions are faced with a very difficult constrained optimization problem - generating as much profit as possible while staying in business by limiting the amount of risk taken.

Title: Technical reserves of non-life insurance in the internal solvency model Author: Bc. Jiří Thomayer Department: Department of Propability and Mathematical Statistics Supervisor: Mgr. Ing. Jakub Mertl Abstract: In this work we study and describe calculation of solvency capital using the standard formula contained in the Directive of the European Union (Solvency II), which should be put into practice in Europe on 1 January 2013. This calcu- lation is described in quantitative impact study 5. We describe a general approach to risk measurement and we show some particular practical measures used to risk measurement. We explain under what conditions the standard formula or its parts can be replaced by internal model. Next, we show disadvantages of using the stan- dard formula and we propose possible internal model to calculate risk premiums and risk reserves in non-life insurance. Finally we apply the proposed model for calculation risk reverses in non-life insurance in practice. Keywords: Standard formula, Risk measurement, Solvency II, Internal model;

<p><strong>Title: </strong>Measuring and handling risk - How different financial institutions face the same problem</p><p><strong>Seminar date: </strong>4^th of June, 2010</p><p><strong> </strong></p><p><strong>Level: </strong>Bachelor thesis in Business Administration, Basic level 300, 15 ECTS</p><p><strong>Authors: </strong>Sarah Rörden and Kristofer Wille</p><p><strong>Supervisor</strong>: Angelina Sundström</p><p><strong>Subject</strong> <strong>terms:</strong> Risk variables, Risk measurement, Risk management, Modern Portfolio Theory, Diversification, Beta</p><p><strong>Target group: </strong>Everyone who has basic knowledge of financial theories and risk principles but lacks the understanding of how they can be used in risk management.</p><p><strong> </strong></p><p><strong>Purpose: </strong>To understand the different Swedish financial institutions’ way of handling and reducing risk in portfolio investing using financial theories.</p><p><strong>Theoretical framework: </strong>The theoretical framework is based on relevant literature about financial theories and risk management, including critical articles.</p><p><strong> </strong></p><p><strong>Method: </strong>A multi-case study has been conducted, built upon empirical data collected through semi-structured interviews at three different financial institutions.</p><p><strong> </strong></p><p><strong>Empiricism: </strong>The study is based on interviews with Per Lundqvist, private banker at Carnegie Investment Bank AB; Erik Dagne, head of risk management department and Joachim Spetz, head of asset management at Erik Penser Bankaktiebolag; and David Lindström, asset manager at Strand Kapitalförvaltning AB.</p><p><strong> </strong></p><p><strong>Conclusion:</strong> There is a practical implementation of the theoretical models chosen for this research. The numbers the financial models generate do not tell one the entire truth about the total risk, therefore the models are used differently at each study object. For a model to hold it has to be transparent, and take each model’s assumptions into account. It all comes down to interpreting the models in an appropriate way.</p>

Traditional inventory models focus on risk-neutral decision makers, i.e., characterizing replenishment strategies that maximize expected total profit, or equivalently, minimize expected total cost over a planning horizon. In this paper, we propose a framework for incorporating risk aversion in multi-period inventory models as well as multi-period models that coordinate inventory and pricing strategies. In each case, we characterize the optimal policy for various measures of risk that have been commonly used in the finance literature. In particular, we show that the structure of the optimal policy for a decision maker with exponential utility functions is almost identical to the structure of the optimal risk-neutral inventory (and pricing) policies. Computational results demonstrate the importance of this approach not only to risk-averse decision makers, but also to risk-neutral decision makers with limited information on the demand distribution. / Singapore-MIT Alliance (SMA)

Title: Measuring and handling risk - How different financial institutions face the same problem Seminar date: 4th of June, 2010   Level: Bachelor thesis in Business Administration, Basic level 300, 15 ECTS Authors: Sarah Rörden and Kristofer Wille Supervisor: Angelina Sundström Subject terms: Risk variables, Risk measurement, Risk management, Modern Portfolio Theory, Diversification, Beta Target group: Everyone who has basic knowledge of financial theories and risk principles but lacks the understanding of how they can be used in risk management.   Purpose: To understand the different Swedish financial institutions’ way of handling and reducing risk in portfolio investing using financial theories. Theoretical framework: The theoretical framework is based on relevant literature about financial theories and risk management, including critical articles.   Method: A multi-case study has been conducted, built upon empirical data collected through semi-structured interviews at three different financial institutions.   Empiricism: The study is based on interviews with Per Lundqvist, private banker at Carnegie Investment Bank AB; Erik Dagne, head of risk management department and Joachim Spetz, head of asset management at Erik Penser Bankaktiebolag; and David Lindström, asset manager at Strand Kapitalförvaltning AB.   Conclusion: There is a practical implementation of the theoretical models chosen for this research. The numbers the financial models generate do not tell one the entire truth about the total risk, therefore the models are used differently at each study object. For a model to hold it has to be transparent, and take each model’s assumptions into account. It all comes down to interpreting the models in an appropriate way.

There are different types of risk, examples include credit risk, liquidity risk and financial risk. In DeMarzo &amp; Berk (2011, s. 293) is a study presented which is based on the yield of different types of financial assets between 1925 and 2009, the study show that a high risk gave substantially higher reward. With the study as a background, it is interesting to study practical risk management within participants of the financial markets of Sweden. In risk management there are several theories about whether risk can be calculated and analyzed with scientific methods in practice. To generate new empirical data a qualitative method was used in the form of interviews. The selection, which was strategic, was based on mailed questionnaire sent to participants of the Swedish fund market. Theory can be problematic to apply in practice, since reality is often simplified in theory, as discussed by Franklin (2004). Franklin’s thoughts are accompanied by Baird (2010) in a similar discussion. The main model of the study is Value at Risk, which is recovered from Hull (2011) but has its origin from the financial company JP Morgan. Other models that are applied in the study are Capital Asset Pricing Model, CAPM, and the Sharpe ratio. There are known critiques against these models, which are discussed in this study. In the study it is shown that all the participants applied the model Value at Risk. The report also indicates that standard deviation has a central role in risk management. All the respondents were well aware of the critique against Value at Risk. To manage the flaws of the model they also used stress tests as a complement. The analysis of the study indicates that practical and theoretical application in many aspects are similar, the most apparent one being Value at Risk. Even though there are some differences, CAPM was indicated to have no practical use for any of the participants. Two vital factors for whether a model can be applied practically are the model’s simplicity and the need for assumptions to correlate with reality. Having completed this study, the conclusion that the participants successfully applied theoretical risk management models in practice can be validated.

An effective risk management program requires reliable risk measurement. Failure to assess inherited risks in mortgage-backed securities in the U.S. market contributed to the financial crisis of 2007–2008, which has prompted government regulators to pay greater attention to controlling risk in banks, investment funds, credit unions, and other financial institutions to prevent bankruptcy and financial crisis in the future. In order to calculate risk in a reliable manner, this thesis has focused on the statistical modeling of expected return and volatility. The primary aim of this study is to propose a framework, based on the probabilistic reduction approach, to reliably quantify market risk using statistical models and historical data. Particular emphasis is placed on the importance of the validity of the probabilistic assumptions in risk measurement by demonstrating how a statistically misspecified model will lead the evaluation of risk astray. The concept of market risk is explained by discussing the narrow definition of risk in a financial context and its evaluation and implications for financial management. After highlighting empirical evidence and discussing the limitations of the ARCH-GARCH-type volatility models using exchange rate and stock market data, we proposed Student's t Autoregressive models to estimate expected return and volatility to measure risk, using Value at Risk (VaR) and Expected Shortfall (ES). The misspecification testing analysis shows that our proposed models can adequately capture the chance regularities in exchange rates and stock indexes data and give a reliable estimation of regression and skedastic functions used in risk measurement. According to empirical findings, the COVID-19 pandemic in the first quarter of 2020 posed an enormous risk to global financial markets. The risk in financial markets returned to levels prior to the COVID-19 pandemic in 2021, after COVID-19 vaccine distribution started in developed countries. / Doctor of Philosophy / Reliable risk measurement is necessary for any effective risk management program. Hence, the primary purpose of this dissertation was to propose a framework to quantify market risk using statistical models and historical data, with a particular emphasis placed on checking the validity of probabilistic assumptions underlying models. After discussing the concept of market risk and its evaluation methods in financial management, we explored the empirical evidence in financial data and highlighted some limitations of other well-known modeling approaches. In order to ameliorate limitations, this study proposed Student's t Autoregressive models to estimate the conditional mean and the conditional variance of the financial variables and use them to measure risk via two popular methods: Value at Risk (VaR) and Expected Shortfall (ES). Further investigation shows that our proposed models can adequately model exchange rates and stock indexes data and give reliable estimations to use in risk measurement. We used our model to quantify risk in global financial markets in recent years. The results show that the COVID-19 pandemic posed an enormous risk to global financial markets in the first quarter of 2020. In 2021, the level of risk in financial markets returned to levels before the COVID-19 pandemic, after COVID-19 vaccine distribution started in developed countries.

La présente étude offre un panorama sur les interactions et les liens qui existent entre la volatilité des taux de change et les échanges internationaux. L’objectif de ce travail est donc de présenter théoriquement cette relation, puis d’examiner empiriquement l’existence de cette relation de causalité entre le commerce international et la variabilité des taux de change. La littérature portant sur la question se considère dans l'ensemble comme contradictoire et supporte plusieurs controverses qui ne nous permettent pas de conclure clairement quant à la relation en question. Nous essayerons de pousser ces recherches un peu plus loin en réexaminant cette évidence pour le canada et en offrant une investigation empirique sur l’existence éventuelle d'un impact significatif de la volatilité sur les flux désagrégées des exportations sectoriels du canada vers son partenaire, les États-Unis. Nous y examinons la réponse empirique de 5 secteurs d’exportations canadiennes aux variations du taux de change réel effectif entre le canada et les États- Unis. Toutefois, nos résultats obtenus ne nous permettent pas de conclure quant à la significativité relative d’un impact de volatilité de taux de change sur les exportations sectoriels désagrégées destinées aux États-Unis. Dans l’ensemble, même si on admet que les signe des coefficients estimés de la variable de risque dans chaque secteur est négatif, nous arrivons à la conclusion que la volatilité ne semble pas avoir un impact statistiquement significatif sur le volume réelle des exportations du Canada vers les États-Unis. / This study provides an overview on the interactions and linkages between the volatility of exchange rates and international trade. The objective of this work is to present this relationship theoretically and examine, empirically the existence of this causal relationship between international trade and exchange rate variability. The literature on the subject considers himself across as contradictory and supports several controversies that do not allow the clear conclusion about the relationship in question. We try to push this research a step further by reviewing the evidence for Canada and providing an empirical investigation on the possible existence of a significant impact of volatility on sectoral disaggregated flows of Canadian exports to its trading partner, the United States. We empirically examine the response of five sectors of Canadian exports to changes in real effective exchange rate between Canada and the United States. However, our results do not allow us to conclude about the significance of an impact on volatility of exchange rates on disaggregated sectoral exports to United States. Overall, even if we admit that the sign of the estimated coefficients of the exchange risk variable in each sector is negative, we reach the conclusion that the volatility does not seem to have a statistically significant impact on the real volume of exports from Canada to the United States.

Baselregelverket är en samling råd och riktlinjer som har som mål att skapa finansiell stabilitet för banker världen över. Det finns i tre omfattningar och efter finanskrisen år 2008 påbörjades ett betydande reformarbete av Basel II efter att banker inte fångade upp riskerna i tillräckligt stor utsträckning. Med ökade kapitalkrav och en förbättrad riskhantering hos bankerna har Baselkommittén som mål att de tidigare bristerna med regelverket inte ska upprepas. Detta har medfört stora interna organisatoriska förändringar för bankerna. Syftet med den här uppsatsen är att undersöka hur finanskrisen år 2008 och reformarbetet av Baselregelverket påverkat chefers handlingsutrymme på svenska banker, där begreppet handlingsutrymme utgår från managerial discretion som handlar om chefers handlingsfrihet under påverkan av externa faktorer. Studien kommer därmed att bidra med en ökad förståelse för regelverket och lyfta fram personliga uppfattningar om hur regelverket har påverkat cheferna.   Kandidatuppsatsen är baserad på en kvalitativ forskningsmetod där vi utförde semi-strukturerade intervjuer med åtta respondenter med chefserfarenhet från svenska banker. Empirin som vi har fått fram tyder på att cheferna upplever ett minskat handlingsutrymme som en påföljd av mer komplexa regelverk. Det har blivit mer komplicerat för cheferna i dag jämfört med innan krisen att styra bankernas dagliga verksamhet på grund av ökade krav på regelefterlevnad och noggrannare uppföljning av riskmätning och kapitalkrav. Vi har även kommit fram till att cheferna upplever förändringar i sitt handlingsutrymme beroende på faktorer som exempelvis bankens storlek och deras införande av olika internmetoder. / The Basel Accords are a collection of advice and recommendations that strives to establish a financial stability of banks all over the world. The accord exists in three versions and after the financial crisis 2008 a considerable reform was established of Basel II due to the fact that previous versions did not accurately handled risks well enough. With the increasing capital requirements and improved risk management at banks, the Basel Committee on Banking Supervision wants to ensure that the previous flaws with the accord will not be repeated. This has resulted in big organizational changes for the banks. The purpose of this paper is to investigate how the financial crisis 2008 and the reform of the Basel Accord that followed have affected the latitude of managerial action of the managers in swedish banks, which is based on managerial discretion that mean changes in managerial roles under influence of external factors. The study will thereby contribute with an increased understanding for this accord and point out personal perceptions of how the regulation have affected the managers.   This bachelor thesis is based on a qualitative research where we performed eight semi-structured interviews with respondents having managerial experiences from swedish banks. The empirical data we have obtained shows that managers perceive a reduced latitude of managerial action as a consequence of more complex regulations. It’s more complicated for managers today considering how it was before the crisis to control the daily operations of the bank because of the increased demand for compliance and a stricter monitoring of risk measurement and capital requirements. We have also concluded that managers are experiencing different changes in the latitude of managerial actions depending on factors such as the bank’s size and how they introduce the various internal methods