The performance of an optimal-weighted portfolio strategy is evaluated when transaction costs are penalized compared to an equal-weighted portfolio strategy. The optimal allocation weights are found by maximizing a modified Sharpe ratio measure each trading day, where modified refers to the expected return of an asset in this context. The leverage of the investment is determined by a conditional expectation estimate of the number of portfolio assets of the next-coming day. A moving window is used to historically measure the transition probabilities of moving from one state to another within this stochastic count process and this is used as an input to the estimator. It is found that the most accurate estimate is the actual trading day’s number of portfolio assets and this is obtained when the size of the moving window is one. Increasing the penalty parameter on transaction costs of selling and buying assets between trading days lowers the aggregated transaction cost and increases the performance of the optimal-weighted portfolio considerably. The best portfolio performance is obtained when at least 50% of the capital is invested equally among the assets when maximizing the modified Sharpe ratio. The optimal-weighted and equal-weighted portfolios are constructed on a daily basis, where the allowed VaR0:05 is €300 000 for each portfolio. This sets the limit on the amount of capital allowed to be invested each trading day, and is determined by empirical VaR0:05 simulations of these two portfolios.

In risk management one important aspect is the allocation of total portfolio risk into its components. This can be done by measuring each components' risk contribution relative to the total risk, taking into account the covariance between components. The measurement procedure is straightforward under assumptions of elliptical distributions but not under the commonly used multivariate log-normal distributions. Two portfolio strategies are considered, the "buy and hold" and the "constant mix" strategy. The profits and losses of the components of a generic portfolio strategy are defined in order to enable a proper definition of risk contribution for the constant mix strategy. Then kernel estimation of risk contribution is performed for both portfolio strategies using Monte Carlo simulation. Further, applications for asset and risk management with risk contributions are discussed in the context of life insurance. / En viktig aspekt inom riskhantering är tilldelning av total portföljrisk till tillångsportföljens beståndsdelar. Detta kan åstadkommas genom att mäta riskbidrag, som även kan ta hänsyn till beroenden mellan risktillgångar. Beräkning av riskbidrag är enkel vid antagande om elliptiska fördelningar så som multivariat normalfördelning, men inte vid antagande om multivariat log-normalfördelning där analytiska formler saknas. Skillnaden mellan riskbidragen inom två portföljstrategier undersöks. Dessa strategier är "buy and hold" och "constant mix" (konstant ombalansering). Tilldelning av resultaten hos de olika beståndsdelarna med en generisk portföljstrategi härleds för att kunna definiera riskbidrag för "constant mix" portföljstrategin. "Kernel estimering" används för att estimera riskbidrag genom simulering. Vidare diskuteras applikationer för tillgångs- och riskhantering inom ramen för livförsäkringsbolag.

Companiesissuing insurance cover, in return for insurance premiums, face the payments ofclaims occurring according to a loss distribution. Hence, capital must be heldby the companies so that they can guarantee the fulfilment of the claims ofeach line of insurance. The increased incidence of insurance insolvencymotivates the birth of new legislations as the European Solvency II Directive.Companies have to determine the required amount of capital and the optimalcapital allocation across the different lines of insurance in order to keep therisk of insolvency at an adequate level. The capital allocation problem may betreated in different ways, starting from the insurance company balance sheet.Here, the running process and efficiency of four methods are evaluated andcompared so as to point out the characteristics of each of the methods. TheValue-at-Risk technique is straightforward and can be easily generated for anyloss distribution. The insolvency put option principle is easily implementableand is sensitive to the degree of default. The capital asset pricing model isone of the oldest reliable methods and still provides very helpful intermediateresults. The Myers and Read marginal capital allocation approach encouragesdiversification and introduces the concept of default value. Applications ofthe four methods to some fictive and real insurance companies are provided. Thethesis further analyses the sensitivity of those methods to changes in the economiccontext and comments how insurance companies can anticipate those changes.

In post-financial crisis times, new legislation in combination with banks’ changed risk aversion has to a great extent changed the proprietary trading to client driven trading, i.e. market making or client facilitation. This type of trading complicates the risk-return dynamics, as the goal is often to minimize risk and achieve profitable commission revenues. This thesis aims to disclose the risk-return tradeoff in a client driven trading environment. This is done by investigating the conditional relation between risk and realized return. As opposed from many studies which proxy the risk with beta or variance, I use a delta-gamma Value at Risk model as the risk proxy, which I also backtest. For the return proxy, I use three different measures; P&L, commission revenues and the sum of these two. A positive tradeoff exists if (i) the return is equally negatively dependent on the risk if the ex post return is negative, as it is positively dependent on the risk if the ex post return is positive and (ii) the average return is significantly positive. For three different client driven trading portfolios tested, I found a positive risk-return tradeoff in one portfolio, between the P&L plus commission revenues and the Value at Risk. However, since a symmetrical conditional relationship between risk and P&L plus commission revenues was found in all portfolios, and the average return was positive, the positive tradeoff would have existed if the average return would have been significantly positive. On the other hand, one could argue that the tradeoff exists, but is not significant. No relation between risk and commission revenues was found. A probable cause to this is the hedging strategies, which would be an interesting topic for further research. / I tiden efter finanskrisen har nya regelverk i kombination med bankers förändrade riskaptit till stor del förändrat den proprietära handeln till klientdriven handel, i.e. ”market making” eller förenklad handel för kund. Denna typ av handel komplicerar dynamiken mellan risk och avkastning, då målet ofta är att minimera risk och nå lönsamma kommissionsintäkter. Denna uppsats ämnar påvisa förhållandet mellan risk och avkastning i en klientdriven handelsmiljö. Detta görs genom att undersöka den betingade relationen mellan risk och realiserad avkastning. Till skillnad från andra studier som använder beta eller varians som riskmått, använder jag en delta-gamma Value at Risk-modell som jag också backtestar. Som avkastningsmått, använder jag tre olika mått; P&L, kommissionsintäkter samt summan av dessa två. En positiv belöning för att bära risk existerar om (i) avkastningen är lika negativt beroende av risken om den realiserade avkastningen är negativ, som den är positivt beroende av risken om den realiserade avkastningen är positiv och (ii) medelvärdet på avkastningen är signifikant positiv. För tre olika klientdrivna portföljer som testats, hittades en positiv belöning för att bära risk endast i en portfölj, mellan P&L plus kommissionsintäkter och Value at Risk. Emellertid, eftersom en symmetrisk systematisk betingad relation mellan risk och P&L plus kommissionsintäkter hittades i alla portföljer, och medelavkastningen var positiv, skulle den positiva belöningen ha funnits om medelavkastningen varit signifikant positiv. Å andra sidan skulle jag kunna hävda att den positiva belöningen finns, men inte är signifikant. Ingen relation mellan risk och kommissionsintäkter hittades. En trolig orsak till detta är hedgnings-strategierna, vilket vore ett intressant ämne för fortsatt forskning.

Stressed Value-at-Risk (VaR) is a statistic used to measure an entity's exposure to market risk by evaluating possible extreme portfolio losses. Stressed VaR scenarios can be used as a metric to describe the state of the financial market and can be used to detect and counter procyclicality by allowing central clearing counterparities (CCP) to increase margin requirements. This thesis aims to implement and evaluate machine learning methods (e.g., neural networks) for selecting stressed VaR scenarios in price return stock datasets where one liquidity day is assumed. The models are implemented to counter the procyclical effects present in NASDAQ's dual lambda method such that the selection maximises the total margin metric. Three machine learning models are implemented together with a labelling algorithm, a supervised and unsupervised multilayer perceptron and a random forest model. The labelling algorithm employs a deviation metric to differentiate between stressed VaR and standard scenarios. The models are trained and tested using 5000 scenarios of price return values from historical stock datasets. The models are tested using visual results, confusion matrix, Cohen's kappa statistic, the adjusted rand index and the total margin metric. The total margin metric is computed using normalised profit and loss values from artificially generated portfolios. The implemented machine learning models and the labelling algorithm manage to counter the procyclical effects evident in the dual lambda method and selected stressed VaR scenarios such that the selection maximise the total margin metric. The random forest model shows the most promise in classifying stressed VaR scenarios, since it manages to maximise the total margin overall.

Hoarding a too large cash reserve is often unfavourable due to lost investment opportunities. Similarly, an insufficient cash reserve can be detrimental, as one might fail to meet payment obligations. Finding the optimal balance is nothing that is done in the blink of an eye, particularly when the underlying variable is stochastic, e.g., the life span of a human being. Resscapital is a fund manager investing in the secondary and tertiary markets for life insurance policies, also known as the life settlements market. They are currently on a mission to set up a closed-end fund where one of the main challenges is balancing the invested capital and the amount of capital set aside for payment obligations. The stochastic nature of life insurance policies entails the difficulty to foresee future premium payments and face value payouts. Without a model forecasting the cash flows, decisions regarding the cash reserve are based on nothing better than a guesstimate. Thus, with the aim to help determine the minimum cash reserve required to cover the payment obligations, this thesis was initiated. By developing a methodology based on general theory, the objective of this thesis is reached and the purpose fulfilled. The proposed model uses Monte Carlo simulation to generate scenarios that eventually creates a distribution of required cash reserves. Following the inversion principle, the remaining lifetime for each and every individual is simulated from their empirical distribution of survival probabilities, respectively. After simulating the occurrences of demise, an algorithm builds up the cash flows for the entire fund term for that specific scenario based on predetermined parameters. Since cash flows stem from both assets and management, the portfolio must be revalued continuously, demanding a gradual evaluation of the cash flows during the fund term. Repeated a large number of times, the quantile corresponding to any confidence level is attained by using a Value at Risk methodology. Analysis of the results and sensitivity analysis on the parameters provides a deeper understanding of the underlying factors, revealing, among other things, that longevity risk for policies with short life expectancy is a key driver of the required cash reserve. Furthermore, validation of the model shows that the results are sufficient and serve the purpose well.

As energy demands increase and energy resources change, the traditional energy system has been upgraded and reconstructed for human society development and sustainability. Considerable studies have been conducted in energy expansion planning and electricity generation operations by mainly considering the integration of traditional fossil fuel generation with renewable generation. Because the energy market is full of uncertainty, we realize that these uncertainties have continuously challenged market design and operations, even a national energy policy. In fact, only a few considerations were given to the optimization of energy expansion and generation taking into account the variability and uncertainty of energy supply and demand in energy markets. This usually causes an energy system unreliable to cope with unexpected changes, such as a surge in fuel price, a sudden drop of demand, or a large renewable supply fluctuation. Thus, for an overall energy system, optimizing a long-term expansion planning and market operation in a stochastic environment are crucial to improve the system's reliability and robustness. As little consideration was paid to imposing risk measure on the power management system, this dissertation discusses applying risk-constrained stochastic programming to improve the efficiency, reliability and economics of energy expansion and electric power generation, respectively. Considering the supply-demand uncertainties affecting the energy system stability, three different optimization strategies are proposed to enhance the overall reliability and sustainability of an energy system. The first strategy is to optimize the regional energy expansion planning which focuses on capacity expansion of natural gas system, power generation system and renewable energy system, in addition to transmission network. With strong support of NG and electric facilities, the second strategy provides an optimal day-ahead scheduling for electric power generation system incorporating with non-generation resources, i.e. demand response and energy storage. Because of risk aversion, this generation scheduling enables a power system qualified with higher reliability and promotes non-generation resources in smart grid. To take advantage of power generation sources, the third strategy strengthens the change of the traditional energy reserve requirements to risk constraints but ensuring the same level of systems reliability In this way we can maximize the use of existing resources to accommodate internal or/and external changes in a power system. All problems are formulated by stochastic mixed integer programming, particularly considering the uncertainties from fuel price, renewable energy output and electricity demand over time. Taking the benefit of models structure, new decomposition strategies are proposed to decompose the stochastic unit commitment problems which are then solved by an enhanced Benders Decomposition algorithm. Compared to the classic Benders Decomposition, this proposed solution approach is able to increase convergence speed and thus reduce 25% of computation times on the same cases.

Optimal portfolios have historically been computed using standard deviation as a risk measure.However, extreme market events have become the rule rather than the exception. To capturetail risk, investors have started to look for alternative risk measures such as Value-at-Risk andConditional Value-at-Risk. This research analyzes the financial model referred to as Markowitz 2.0 and provides historical context and perspective to the model and makes a mathematicalformulation. Moreover, practical implementation is presented and an optimizer that capturesthe risk of non-extreme events is constructed, which meets the needs of more customized investment decisions, based on investment preferences. Optimal portfolios are generated and anefficient frontier is made. The results obtained are then compared with those obtained throughthe mean-variance optimization framework. As concluded from the data, the optimal portfoliowith the optimal weights generated performs better regarding expected portfolio return relativeto the risk level for the investment.

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