This thesis compares insurance premium principles with current financial risk paradigms and uses distorted probabilities, a recent development in premium principle literature, to synthesize the current models for financial risk measures in banking and insurance. This work attempts to broaden the definition of value-at-risk beyond the percentile measures. Examples are used to show how the percentile measure fails to give consistent results, and how it can be manipulated. A new class of consistent risk measures is investigated.

This thesis investigates robust techniques for mean-variance (MV) portfolio optimization problems under the estimation risk in mean return. We evaluate the performance of the optimal portfolios generated by the min-max robust MV portfolio optimization model. With an ellipsoidal uncertainty set based on the statistics of the sample mean estimates, minmax robust portfolios equal to the ones from the standard MV model based on the nominal mean estimates but with larger risk aversion parameters. With an interval uncertainty set for mean return, min-max robust portfolios can vary significantly with the initial data used to generate the uncertainty set. In addition, by focusing on the worst-case scenario in the mean return uncertainty set, min-max robust portfolios can be too conservative and unable to achieve a high return. Adjusting the conservatism level of min-max robust portfolios can only be achieved by excluding poor mean return scenarios from the uncertainty set, which runs counter to the principle of min-max robustness. We propose a CVaR robust MV portfolio optimization model in which the estimation risk is measured by the Conditional Value-at-Risk (CVaR). We show that, using CVaR to quantify the estimation risk in mean return, the conservatism level of CVaR robust portfolios can be more naturally adjusted by gradually including better mean return scenarios. Moreover, we compare min-max robust portfolios (with an interval uncertainty set for mean return) and CVaR robust portfolios in terms of actual frontier variation, portfolio efficiency, and portfolio diversification. Finally, a computational method based on a smoothing technique is implemented to solve the optimization problem in the CVaR robust model. We numerically show that, compared with the quadratic programming (QP) approach, the smoothing approach is more computationally efficient for computing CVaR robust portfolios.

Investmentföretag har funnits sedan urminnes tider men har under senare år ofta fått stå tillbaka som investeringsalternativ till fördel för aktiefonder. Detta är lite motsägelsefullt då svenska investmentföretagen historiskt har haft en högre avkastning än den svenska aktiefondförvaltaren. Större delen av forskningen kring investmentföretag har fokuserat på substansrabatten. Vi fann väldigt få studier som berört investmentföretagens risktagande, speciellt ur ett portföljperspektiv. För att underlätta för den individuella investeraren ville vi använda ett riskmått som är lätt att förstå. Valet föll därför på Value at Risk (VaR) som vi anser ger ett lättförståeligt mått på risken i en portfölj samtidigt som det valideras genom Basel II. Då investmentföretagen är väldigt heterogena med avseende på deras portföljsammansättningar och investeringsstrategier valde vi att genomföra en fallstudie på Industrivärden och Svolder. Valet av dessa företag möjliggjorde också en jämförelse mellan ett större och mindre investmentföretag. Vi ville undersöka och jämföra hur deras risktagande påverkas och förklaras utifrån olika faktorer, med utgångspunkt från den tidigare omkringliggande forskningen. De teoretiska utgångspunkterna hämtades från fyra olika områden, risk och portföljvalsteori, Behavioural Finance, Corporate Governance och makroekonomisk statistik. Vi valde att genomföra en kvantitativ studie för att undersöka Industrivärdens och Svolders risktagande. Studien är baserad på investmentföretagens kvartalsrapporter mellan 2000 till 2011. Utifrån vår referensram definierade vi 13 olika variabler som statistiskt prövades mot risktagandet med hjälp av multipla regressioner. Från våra resultat kunde vi konstatera att den makroekonomiska statistiken förklarade mest av investmentföretagens risktagande. Gemensamt för båda investmentföretagen var att industriproduktionen, Fed fund rate och konjunkturbarometern visade på ett signifikant samband med risktagande. Vi fann även indikationer på att den geografiska exponeringen för deras portföljer hade betydelse för att förklara risktagandet. Vår studie pekade också på att investmentföretagens risktagande visade upp en trend och korrelerade negativt med börsmarknaden.

The purpose of this thesis is to examine whether Swedish Equity L/S hedge funds present a lower market risk than the index S&P Europe 350 over our holding period using a GARCH/EGARCH Value-at-Risk model. The sample consists of 96 monthly observa- tions between March 2004 and February 2012. The examination shows that the hedge funds in general hold a lower market risk than the index for the next holding period and al- so present a lower estimated loss if our VaR loss is exceeded. This implies that hedge funds would be a good choice for investors to have in a portfolio to reduce the risk.

In this paper we use model-free estimates of daily exchange rate volatilities employing high-frequency intraday data, known as Realized Volatility, which is then forecasted with ARMA-models and used to produce one-day-ahead Value-at-Risk predictions. The forecasting accuracy of the method is contrasted against the more widely used ARCH-models based on daily squared returns. Our results indicate that the ARCH-models tend to underestimate the Value-at-Risk in foreign exchange markets compared to models using Realized Volatility

The aim of the thesis is to identify an appropriate model in forecasting Value-at-Risk on a morevolatile period than that one from which the model is estimated. We estimate 1-day-ahead and10-days-ahead Value-at-Risk on a number of exchange rates. The Value-at-Risk estimates arebased on three models combined with three distributional assumptions of the innovations, andthe evaluations are made with Kupiec's (1995) test for unconditional coverage. The data rangesfrom January 1st 2006 through June 30th 2011. The results suggest that the GARCH(1,1) andGJR-GARCH(1,1) with normally distributed innovations are models adequately capturing theconditional variance in the series.

It is a well-known fact that macro-economic conditions, such as prices of commodities (e.g. oil, cement and steel) affect the cost of construction projects. In a volatile market environment, highway agencies often pass such risk to contractors using fixed-price contracts. In turn, the contractors respond by adding premiums in bid prices. If the contractors overprice the risk, the price of fixed-price contract could exceed the price of the contract with adjustment clauses. Consequently, highway agencies have the opportunity to design a contract that not only reduces the future risk of exposure, but also reduces the initial contract price. The main goal of this dissertation is to investigate the impact of commodity price risk on construction cost and the optimal risk hedging of such risks using price adjustment clauses. More specifically, the objective of the dissertation is to develop models that can help highway agencies manage commodity price risks. In this dissertation, a weighted least square regression model is used to estimate the risk premium; both univariate and vector time series models are estimated and applied to simulate changes in commodity prices over time, including the effect of correlation; while the genetic algorithm is used as a solution approach to a multi-objective optimization formulation. The data set used in this dissertation consists of TxDOT bidding data, market-based data including New York Mercantile Exchange (NYMEX) future options data, and Engineering News-Record (ENR) material cost index data. The results of this dissertation suggest that the optimal risk mitigation actions are conditional on owners' risk preferences, correlation among the prices of commodities, and volatility of the market.

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This dissertation includes two topics. The first topic focuses on the problem of investor optimization of dynamic asset allocation to maximize expected utility under the value at risk (VaR) constraint. Different to previous researches, this study considers a common realistic case where the VaR horizon is equal to the whole investment horizon without a complete market constraint. Since the problem cannot be solved using the standard dynamic programming method or the martingale method, this study particularly provides an algorithm to solve this difficult problem. Similar to the mean-variance frontier suggested by Markowitz (1952), this study draws the frontiers of dynamic and static asset allocations under the VaR constraint. The analytical results clearly show that the dynamic asset allocations are more efficient than the static asset allocations. The second topic designs an optimal insurance policy form endogenously, assuming the objective of the insured is to maximize expected final wealth under the VaR constraint. The optimal insurance policy can be replicated using three options, including a long call option with a small strike price, a short call option with a large strike price, and a short cash-or-nothing call option. Moreover, expected wealth is increasing and concave in VaR and in significance level. Finally, Mean-VaR Frontiers are drawn, and reveal that the optimal insurance is more efficient than alternative insurance forms.

Many financial time series show heavy tail behavior. Such tail characteristic is important for risk management. In this research, we focus on the calculation of Value-at-Risk (VaR) for portfolios of financial assets. We consider nonlinear autoregressive models with heavy tail innovations to model the return. Predictive distribution of the return are used to compute the VaR of the portfolios of financial assets. Examples are also given to compare the VaR computed by our approach with those by other methods.