5,728 research outputs found

    Robust and Multi-objective Portfolio Selection

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    In this thesis, robust and multi-objective portfolio selection problem will be studied. New models and computational algorithms will be developed to solve the proposed models. In particularly, we have studied multi-objective portfolio selection with inexact information on investment return and covariance matrix. The problems have been transformed into easily solvable problems through theoretical analysis. Numerical experiments are presented to validate the methods

    Portfolio Selection under Distributional Uncertainty: A Relative Robust CVaR in Portfolio Management

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    Robust optimization, one of the most popular topics in the field of optimization and control since the late 1990s, deals with an optimization problem involving uncertain parameters. In this paper, we consider the relative robust conditional value-at-risk portfolio selection problem where the underlying probability distribution of portfolio return is only known to belong to a certain set. Our approach not only takes into account the worst-case scenarios of the uncertain distribution, but also pays attention to the best possible decision with respect to each realization of the distribution. We also illustrate how to construct a robust portfolio with multiple experts (priors) by solving a sequence of linear programs or a second-order cone program

    Review of stochastic differential equations in statistical arbitrage pairs trading

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    The use of stochastic differential equations offers great advantages for statistical arbitrage pairs trading. In particular, it allows the selection of pairs with desirable properties, e.g., strong mean-reversion, and it renders traditional rules of thumb for trading unnecessary. This study provides an exhaustive survey dedicated to this field by systematically classifying the large body of literature and revealing potential gaps in research. From a total of more than 80 relevant references, five main strands of stochastic spread models are identified, covering the ‘Ornstein–Uhlenbeck model’, ‘extended Ornstein–Uhlenbeck models’, ‘advanced mean-reverting diffusion models’, ‘diffusion models with a non-stationary component’, and ‘other models’. Along these five main categories of stochastic models, we shed light on the underlying mathematics, hereby revealing advantages and limitations for pairs trading. Based on this, the works of each category are further surveyed along the employed statistical arbitrage frameworks, i.e., analytic and dynamic programming approaches. Finally, the main findings are summarized and promising directions for future research are indicated

    Product portfolio analysis

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    Buy, Sell or Rent the Farm: An Agent Based Simulation of Farm Succession and Land Valuation

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    The impact of widespread farm ownership by large investors in Canada could be influential and remains uncertain. In fact, there are sound financial reasons for buying farmland as an investment, including diversification benefits available to investment portfolios. Studies have found that the correlation between farmland price yield and the yields of major financial assets, such as stocks, bonds and real estate, are consistently negative. On the other hand, the prime objectives of many farm family businesses are “to maintain control and pass on a secure and sound business to the next generation” (Hay and Morris 1984, Errington 2002). In Western Canada, farmland is generally retained within the family by succession because of strong emotional and economic linkages. However, very little prior research has examined the long-term effect of interactions between these two options for Prairie farmland transition. Due to the complexity of the problem, the agent based simulation model (ABSM) is one of the few feasible ways for this issue. The simulation model developed in this study builds upon Anderson’s (2012) work simulating farming activity in Canadian Agricultural Region 1A in Saskatchewan, using the Repast© software. Two extensions or modules for the farm simulation are developed in this thesis, comprising farm succession as well as the presence of institutional investors who purchase farmland as a financial asset in order to diversify aggregate risk in their portfolio. Thirty years of farming and investing performance are simulated in four different scenarios to examine the effects of various levels of institutional investor participation. Institutional investors are found to elevate farmland prices from between 15% to 40% across different scenarios, while farmers ultimately tend to lease slightly more land to compensate and expand their farms. Meanwhile, the total number of farms in the region fall over time, while larger individual farms emerge over the simulated period, both with or without investors. Based on this simulated evidence, we conclude that the overall impact of institutional investors on future farming will be subtle, and continued farm success here is contingent on farmers being willing to rely more on rental land for farm expansion

    Essays in Robust and Data-Driven Risk Management

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    Risk defined as the chance that the outcome of an uncertain event is different than expected. In practice, the risk reveals itself in different ways in various applications such as unexpected stock movements in the area of portfolio management and unforeseen demand in the field of new product development. In this dissertation, we present four essays on data-driven risk management to address the uncertainty in portfolio management and capacity expansion problems via stochastic and robust optimization techniques.The third chapter of the dissertation (Portfolio Management with Quantile Constraints) introduces an iterative, data-driven approximation to a problem where the investor seeks to maximize the expected return of his/her portfolio subject to a quantile constraint, given historical realizations of the stock returns. Our approach involves solving a series of linear programming problems (thus) quickly solves the large scale problems. We compare its performance to that of methods commonly used in finance literature, such as fitting a Gaussian distribution to the returns. We also analyze the resulting efficient frontier and extend our approach to the case where portfolio risk is measured by the inter-quartile range of its return. Furthermore, we extend our modeling framework so that the solution calculates the corresponding conditional value at risk CVaR) value for the given quantile level.The fourth chapter (Portfolio Management with Moment Matching Approach) focuses on the problem where a manager, given a set of stocks to invest in, aims to minimize the probability of his/her portfolio return falling below a threshold while keeping the expected portfolio returnno worse than a target, when the stock returns are assumed to be Log-Normally distributed. This assumption, common in finance literature, creates computational difficulties. Because the portfolio return itself is difficult to estimate precisely. We thus approximate the portfolio re-turn distribution with a single Log-Normal random variable by the Fenton-Wilkinson method and investigate an iterative, data-driven approximation to the problem. We propose a two-stage solution approach, where the first stage requires solving a classic mean-variance optimization model, and the second step involves solving an unconstrained nonlinear problem with a smooth objective function. We test the performance of this approximation method and suggest an iterative calibration method to improve its accuracy. In addition, we compare the performance of the proposed method to that obtained by approximating the tail empirical distribution function to a Generalized Pareto Distribution, and extend our results to the design of basket options.The fifth chapter (New Product Launching Decisions with Robust Optimization) addresses the uncertainty that an innovative firm faces when a set of innovative products are planned to be launched a national market by help of a partner company for each innovative product. Theinnovative company investigates the optimal period to launch each product in the presence of the demand and partner offer response function uncertainties. The demand for the new product is modeled with the Bass Diffusion Model and the partner companies\u27 offer response functions are modeled with the logit choice model. The uncertainty on the parameters of the Bass Diffusion Model and the logic choice model are handled by robust optimization. We provide a tractable robust optimization framework to the problem which includes integer variables. In addition, weprovide an extension of the proposed approach where the innovative company has an option to reduce the size of the contract signed by the innovative firm and the partner firm for each product.In the sixth chapter (Log-Robust Portfolio Management with Factor Model), we investigate robust optimization models that address uncertainty for asset pricing and portfolio management. We use factor model to predict asset returns and treat randomness by a budget of uncertainty. We obtain a tractable robust model to maximize the wealth and gain theoretical insights into the optimal investment strategies

    Multistage decisions and risk in Markov decision processes: towards effective approximate dynamic programming architectures

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    The scientific domain of this thesis is optimization under uncertainty for discrete event stochastic systems. In particular, this thesis focuses on the practical implementation of the Dynamic Programming (DP) methodology to discrete event stochastic systems. Unfortunately DP in its crude form suffers from three severe computational obstacles that make its imple-mentation to such systems an impossible task. This thesis addresses these obstacles by developing and executing practical Approximate Dynamic Programming (ADP) techniques. Specifically, for the purposes of this thesis we developed the following ADP techniques. The first one is inspired from the Reinforcement Learning (RL) literature and is termed as Real Time Approximate Dynamic Programming (RTADP). The RTADP algorithm is meant for active learning while operating the stochastic system. The basic idea is that the agent while constantly interacts with the uncertain environment accumulates experience, which enables him to react more optimal in future similar situations. While the second one is an off-line ADP procedure These ADP techniques are demonstrated on a variety of discrete event stochastic systems such as: i) a three stage queuing manufacturing network with recycle, ii) a supply chain of the light aromatics of a typical refinery, iii) several stochastic shortest path instances with a single starting and terminal state and iv) a general project portfolio management problem. Moreover, this work addresses, in a systematic way, the issue of multistage risk within the DP framework by exploring the usage of intra-period and inter-period risk sensitive utility functions. In this thesis we propose a special structure for an intra-period utility and compare the derived policies in several multistage instances.Ph.D.Committee Chair: Jay H. Lee; Committee Member: Martha Grover; Committee Member: Matthew J. Realff; Committee Member: Shabbir Ahmed; Committee Member: Stylianos Kavadia

    Robust and Constrained Portfolio Optimization using Multiobjective Evolutionary Algorithms

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    Optimization plays an important role in many areas of science, management,economics and engineering. Many techniques in mathematics and operation research are available to solve such problems. However these techniques have many shortcomings to provide fast and accurate solution particularly when the optimization problem involves many variables and constraints. Investment portfolio optimization is one such important but complex problem in computational finance which needs effective and efficient solutions. In this problem each available asset is judiciously selected in such a way that the total profit is maximized while simultaneously minimizing the total risk. The literature survey reveals that due to non availability of suitable multi objective optimization tools, this problem is mostly being solved by viewing it as a single objective optimization problem

    Markowitz-based cardinality constrained portfolio selection using Asexual Reproduction Optimization (ARO)

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    The Markowitz-based portfolio selection turns to an NP-hard problem when considering cardinality constraints. In this case, existing exact solutions like quadratic programming may not be efficient to solve the problem. Many researchers, therefore, used heuristic and metaheuristic approaches in order to deal with the problem. This work presents Asexual Reproduction Optimization (ARO), a model free metaheuristic algorithm inspired by the asexual reproduction, in order to solve the portfolio optimization problem including cardinality constraint to ensure the investment in a given number of different assets and bounding constraint to limit the proportions of fund invested in each asset. This is the first time that this relatively new metaheuristic is in the field of portfolio optimization, and we show that ARO results in better quality solutions in comparison with some of the well-known metaheuristics stated in the literature. To validate our proposed algorithm, we measured the deviation of obtained results from the standard efficient frontier. We report our computational results on a set of publicly available benchmark test problems relating to five main market indices containing 31, 85, 89, 98, and 225 assets. These results are used in order to test the efficiency of our proposed method in comparison to other existing metaheuristic solutions. The experimental results indicate that ARO outperforms Genetic Algorithm(GA), Tabu Search (TS), Simulated Annealing (SA), and Particle Swarm Optimization (PSO) in most of test problems. In terms of the obtained error, by using ARO, the average error of the aforementioned test problems is reduced by approximately 20 percent of the minimum average error calculated for the above-mentioned algorithms
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