Wir untersuchen eine zeitstetige Variante des zeitlich diskreten Modells von Jarrow für einen illiquiden Finanzmarkt. In dieser kann mit einem Bond und einer Aktie gehandelt werden. Während im Standardmodell eines liquiden Finanzmarktes die stochastische Dynamik des Aktienpreises durch ein festes Semimartingal modelliert wird, hängt der Aktienpreis in unserem Modell einerseits von einem fundamentalen Semimartingal, das sich als kumulative Nachfrage vieler kleiner Investoren interpretieren läßt, andererseits aber auch monoton wachsend vom Aktienbestand der Handelsstrategie eines ökonomischen Agenten ab. Wegen des damit verbundenen Rückkopplungseffekts ist es, im Gegensatz zu liquiden Finanzmärkten, nicht möglich, die bekannten Darstellungssätze der Stochastischen Analysis zu verwenden, um Zufallsvariablen als stochastische Integrale bezüglich des Prozesses der abdiskontierten Aktienpreise darzustellen und auf dieser Basis Absicherungsstrategien für Derivate zu konstruieren. Wir definieren den realisierbaren Portfoliowert als den abdiskontierten Erlös einer idealisierten, in einem gewissen Sinne optimalen, Liquidationsstrategie. Mit Hilfe der Ito-Formel leiten wir eine Zerlegung der Dynamik des realisierbaren Portfoliowertes selbstfinanzierender Strategien in ein stochastisches Integral und einen fallenden Prozeß her. Dabei ist der Integrator des stochastischen Integrals ein von der betrachteten Strategie unabhängiges lokales Martingal unter einem äquivalenten Martingalmaß . Aus dieser Zerlegung ergibt sich ein Beweis für die Arbitragefreiheit des Modells. Der Zerlegungssatz zeigt insbesondere, daß der realisierbare Portfoliowert stetiger Strategien von beschränkter Variation ein lokales Martingal unter einem äquivalenten Martingalmaß ist. Wir beweisen deshalb einen Approximationssatz für stochastische Integrale, der es erlaubt, sich bei der Absicherung von Derivaten auf solche Strategien zu beschränken. Durch Kombination des Approximationssatzes und des Zerlegungssatzes können wir Superreplikationspreise von Derivaten bestimmen und die relevanten Portfoliooptimierungsprobleme lösen. / We study a continuous time version of Jarrows model for an illiquid financial market in discrete time. In this model one can trade with a bond and a stock. In standard models for liquid financial markets, the stochastic dynamic of stock prices is modelled as a given semimartingale. In contrast, stock prices in our model depend on a fundamental semimartingale that can be interpreted as the cumulative demand of small investors and, in a monotone increasing way, on the strategy of an economic agent. Because of the resulting feedback effects, it is no longer possible to use the well known representation theorems of stochastic analysis to write random variables as stochastic integrals with respect to discounted stock prices and to use this to find hedging strategies for derivatives. We define realisable portfolio wealth as the discounted proceeds of an idealised liquidation strategy that is optimal in a certain sense. Using Itos formula, we can write the dynamics of the realisable portfolio wealth of self-financing strategies as the sum of a stochastic integral and a decreasing process. The integrator in the stochastic integral is a local martingale under an equivalent martingale measure that does not depend on the self-financing strategy. This decomposition yields a proof for the fact that our model is arbitrage free. The decomposition theorem shows that the realisable portfolio wealth of continuous strategies of bounded variation is a local martingale under an equivalent martingale measure. Therefore, we proof an approximation result for stochastic integrals that shows that we can restrict the search for hedging strategies to continuous strategies of bounded variation. By combining the approximation result and the decomposition theorem we can calculate superreplication prices for derivatives and solve the relevant portfolio optimisation problems.

The shareholders of E&P companies evaluate the future performance of these companies in terms of multiple performance attributes. Hence, E&P decision makers have the task of allocating limited resources to available project proposals to deliver the best performance on these various attributes. Additionally, the performance of these proposals on these attributes is uncertain and the attributes of the various proposals are usually correlated. As a result of the above, the E&P portfolio optimisation decision setting is characterised by multiple attributes with uncertain future performance. Most recent contributions in the E&P portfolio optimisation arena seek to adapt modern financial portfolio theory concepts to the E&P project portfolio selection problem. These contributions generally focus on understanding the tradeoffs between risk and return for the attribute NPV while acknowledging the presence of correlation among the assets of the portfolio. The result is usually an efficient frontier where one objective is set over the expected value of the NPV and the other is set over a risk metric calculated from the same attribute where, typically, the risk metric has a closed form solution (e.g., variance, standard deviation, semi-standard deviation). However, this methodology fails to acknowledge the presence of multiple attributes in the E&P decision setting. To fill this gap, this thesis proposes a decision support model to optimise risk and return objectives extracted from the NPV attribute and from other financial and/or operational attributes simultaneously. The result of this approach is an approximate Pareto front that explicitly shows the tradeoffs among these objectives whilst honouring intra-project and inter-project correlations. Intra-project correlations are incorporated into the optimisation by integrating the single project models to the portfolio model to be optimised. Inter-project correlation is included by modelling of the oil price a global variable. Additionally, the model uses a multi-objective simulation-optimisation approach and hence it overcomes the need of using risk metrics with closed form solutions. The model is applied to a set of realistic hypothetical offshore E&P projects. The results show the presence of complex relationships among the objectives in the approximate Pareto set. The ability of the method to unveil these relationships hopes to bring more insight to the decision makers and hence promote better investment decisions in the E&P industry. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1320463 / Thesis (M.Eng.Sc.) -- University of Adelaide, Australian School of Petroleum, 2008

The master's thesis is focused on Stock portfolio optimalization on Czech capital market. The analysis of each stock, estimation and portfolio optimalization proposal are included. In the practical part the Fundamental analysis is applied. The portfolio optimalization is estemated by portfolio theory which is consist in the relationship between stock price and market trends represents by PX Index and expressing correlation of them by beta coefficient.

In this thesis we investigate the application of two heuristic methods, genetic algorithms and tabu/scatter search, to the optimisation of realistic portfolios. The model is based on the classical mean-variance approach, but enhanced with floor and ceiling constraints, cardinality constraints and nonlinear transaction costs which include a substantial illiquidity premium, and is then applied to a large I 00-stock portfolio. It is shown that genetic algorithms can optimise such portfolios effectively and within reasonable times, without extensive tailoring or fine-tuning of the algorithm. This approach is also flexible in not relying on any assumed or restrictive properties of the model and can easily cope with extensive modifications such as the addition of complex new constraints, discontinuous variables and changes in the objective function. The results indicate that that both floor and ceiling constraints have a substantial negative impact on portfolio performance and their necessity should be examined critically relative to their associated administration and monitoring costs. Another insight is that nonlinear transaction costs which are comparable in magnitude to forecast returns will tend to diversify portfolios; the effect of these costs on portfolio risk is, however, ambiguous, depending on the degree of diversification required for cost reduction. Generally, the number of assets in a portfolio invariably increases as a result of constraints, costs and their combination. The implementation of cardinality constraints is essential for finding the bestperforming portfolio. The ability of the heuristic method to deal with cardinality constraints is one of its most powerful features. / Decision Sciences / M. Sc. (Operations Research)

<p>The topic of the research in this dissertation is the application of machine<br />learning in solving problems characteristic to biosystems, with special<br />emphasis on agriculture. Firstly, an innovative regression algorithm based on<br />big data was presented, that was used for yield prediction. The predictions<br />were then used as an input for the improved portfolio optimisation algorithm,<br />so that appropriate soybean varieties could be selected for fields with<br />distinctive parameters. Lastly, a multi-objective optimisation problem was set<br />up and solved using a novel method for categorical evolutionary algorithm<br />based on NSGA-III.</p> / <p>Предмет истраживања докторске дисертације је примена машинског учења у решавању проблема карактеристичних за биосистемe са нагласком на пољопривреду. Најпре је представљен иновативни алгоритам за регресију који је примењен на великој количини података како би се са предиковали приноси. На основу предикција одабране су одговарајуће сорте соје за њиве са одређеним карактеристикама унапређеним алгоритмом оптимизације портфолија. Напослетку је постављен оптимизациони проблем одређивања сетвене структуре са вишеструким функцијама циља који је решен иновативном методом, категоричким еволутивним алгоритмом заснованом на NSGA-III алгоритму.</p> / <p>Predmet istraživanja doktorske disertacije je primena mašinskog učenja u rešavanju problema karakterističnih za biosisteme sa naglaskom na poljoprivredu. Najpre je predstavljen inovativni algoritam za regresiju koji je primenjen na velikoj količini podataka kako bi se sa predikovali prinosi. Na osnovu predikcija odabrane su odgovarajuće sorte soje za njive sa određenim karakteristikama unapređenim algoritmom optimizacije portfolija. Naposletku je postavljen optimizacioni problem određivanja setvene strukture sa višestrukim funkcijama cilja koji je rešen inovativnom metodom, kategoričkim evolutivnim algoritmom zasnovanom na NSGA-III algoritmu.</p>

Portfolio optimisation has a number of constraints resulting from some practical matters and regulations. The closed-form mathematical solution of portfolio optimisation problems usually cannot include these constraints. Exhaustive search to reach the exact solution can take prohibitive amount of computational time. Portfolio optimisation models are also usually impaired by the estimation error problem caused by lack of ability to predict the future accurately. A number of Multi-Objective Genetic Algorithms are proposed to solve the problem with two objectives subject to cardinality constraints, floor constraints and round-lot constraints. Fuzzy logic is incorporated into the Vector Evaluated Genetic Algorithm (VEGA) to but solutions tend to cluster around a few points. Strength Pareto Evolutionary Algorithm 2 (SPEA2) gives solutions which are evenly distributed portfolio along the effective front while MOGA is more time efficient. An Evolutionary Artificial Neural Network (EANN) is proposed. It automatically evolves the ANN's initial values and structures hidden nodes and layers. The EANN gives a better performance in stock return forecasts in comparison with those of Ordinary Least Square Estimation and of Back Propagation and Elman Recurrent ANNs. Adaptation algorithms for selecting a pair of forecasting models, which are based on fuzzy logic-like rules, are proposed to select best models given an economic scenario. Their predictive performances are better than those of the comparing forecasting models. MOGA and SPEA2 are modified to include a third objective to handle model risk and are evaluated and tested for their performances. The result shows that they perform better than those without the third objective.

In this thesis we investigate the application of two heuristic methods, genetic algorithms and tabu/scatter search, to the optimisation of realistic portfolios. The model is based on the classical mean-variance approach, but enhanced with floor and ceiling constraints, cardinality constraints and nonlinear transaction costs which include a substantial illiquidity premium, and is then applied to a large I 00-stock portfolio. It is shown that genetic algorithms can optimise such portfolios effectively and within reasonable times, without extensive tailoring or fine-tuning of the algorithm. This approach is also flexible in not relying on any assumed or restrictive properties of the model and can easily cope with extensive modifications such as the addition of complex new constraints, discontinuous variables and changes in the objective function. The results indicate that that both floor and ceiling constraints have a substantial negative impact on portfolio performance and their necessity should be examined critically relative to their associated administration and monitoring costs. Another insight is that nonlinear transaction costs which are comparable in magnitude to forecast returns will tend to diversify portfolios; the effect of these costs on portfolio risk is, however, ambiguous, depending on the degree of diversification required for cost reduction. Generally, the number of assets in a portfolio invariably increases as a result of constraints, costs and their combination. The implementation of cardinality constraints is essential for finding the bestperforming portfolio. The ability of the heuristic method to deal with cardinality constraints is one of its most powerful features. / Decision Sciences / M. Sc. (Operations Research)

Diplomová práce se zabývá aplikací vybraných metod umělé inteligence v prostředí kapitálových, potažmo akciových, trhů. Konkrétně se zaměřuje na využití umělých neuronových sítí pro predikci trendu a na možnost aplikace genetických algoritmů k řešení problému optimalizace investičního portfolia. Obsahuje návrh řešení uvedených problémů v praxi. Návrhy jsou koncipovány ve formě modelů zpracovaných ve vývojovém prostředí Matlab.

Portfolio optimisation has a number of constraints resulting from some practical matters and regulations. The closed-form mathematical solution of portfolio optimisation problems usually cannot include these constraints. Exhaustive search to reach the exact solution can take prohibitive amount of computational time. Portfolio optimisation models are also usually impaired by the estimation error problem caused by lack of ability to predict the future accurately. A number of Multi-Objective Genetic Algorithms are proposed to solve the problem with two objectives subject to cardinality constraints, floor constraints and round-lot constraints. Fuzzy logic is incorporated into the Vector Evaluated Genetic Algorithm (VEGA) to but solutions tend to cluster around a few points. Strength Pareto Evolutionary Algorithm 2 (SPEA2) gives solutions which are evenly distributed portfolio along the effective front while MOGA is more time efficient. An Evolutionary Artificial Neural Network (EANN) is proposed. It automatically evolves the ANN¿s initial values and structures hidden nodes and layers. The EANN gives a better performance in stock return forecasts in comparison with those of Ordinary Least Square Estimation and of Back Propagation and Elman Recurrent ANNs. Adaptation algorithms for selecting a pair of forecasting models, which are based on fuzzy logic-like rules, are proposed to select best models given an economic scenario. Their predictive performances are better than those of the comparing forecasting models. MOGA and SPEA2 are modified to include a third objective to handle model risk and are evaluated and tested for their performances. The result shows that they perform better than those without the third objective.

Modern financial asset pricing theory is a broad, and at times, complex field. The literature review in this study covers many of the asset pricing techniques including factor models, random walk models, correlation models, Bayesian methods, autoregressive models, moment-matching models, stochastic jumps and mean reversion models. An important topic in finance is portfolio opti-misation with respect to risk and reward such as the mean variance optimisation introduced by Markowitz (1952). This study covers optimisation techniques such as single period mean variance optimisation, optimisation with risk aversion, multi-period stochastic programs, two-fund separa- tion theory, downside optimisation techniques and multi-period optimisation such as the Bellman dynamic programming model. The question asked in this study is, in the context of investing for South African individuals in a multi-asset portfolio, whether an active investment strategy is signi cantly di erent from a passive investment strategy. The passive strategy is built using stochastic programming with moment matching methods for non-Gaussian asset class distributions. The strategy is optimised in a framework using a downside risk metric, the conditional variance at risk. The active strategy is built with forward forecasts for asset classes using the time-varying transitional-probability Markov regime switching model. The active portfolio is finalised by a dynamic optimisation using a two-stage stochastic programme with recourse, which is solved as a large linear program. A hypothesis test is used to establish whether the results of two strategies are statistically different. The performance of the strategies are also reviewed relative to multi-asset peer rankings. Lastly, we consider whether the findings reveal information on the degree of effi ciency in the market place for multi-asset investments for the South African investor. / Operations Management / M. Sc. (Operations Research)