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History of Modelling Languages
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Portfolio Optimization & Asset Allocation
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Abstract: Modern Portfolio Theory (MPT) is based upon the classical Markowitz model which uses variance as a risk measure. A generalisation of this approach leads to mean-risk models, in which a return distribution is characterised by the expected value of return (desired to be large) and a “risk” value (desired to be kept small). Portfolio choice is made by solving an optimization problem, in which the portfolio risk is minimised and a desired level of expected return is specified as a constraint. The need to penalize different undesirable aspects of the return distribution led to the proposal of alternative risk measures, notably those penalising only the downside part (adverse) and not the upside (potential). The downside risk considerations constitute the basis of the Post Modern Portfolio Theory (PMPT). Examples of such risk measures are lower partial moments, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). We revisit these risk measures and the resulting mean-risk models. We discuss alternative models for portfolio selection, their choice criteria and the evolution of MPT to PMPT which incorporates: utility maximisation and stochastic dominance.
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Abstract: Second-order stochastic dominance (SSD) is widely recognised as an important decision criterion in portfolio selection. Unfortunately, stochastic dominance models are known to be very demanding from a computational point of view. In this paper we consider two classes of models which use SSD as a choice criterion. The first, proposed by Dentcheva and Ruszczy4nski (J Bank Finance 30:433451, 2006), uses a SSD constraint, which can be expressed as integrated chance constraints (ICCs). The second, proposed by Roman et al. (Math Program, Ser B 108:541569, 2006) uses SSD through a multi-objective formulation with CVaR objectives. Cutting plane representations and algorithms were proposed by Klein Haneveld and Van der Vlerk (Comput Manage Sci 3:245269, 2006) for ICCs, and by K|nzi-Bay and Mayer (Comput Manage Sci 3:327, 2006) for CVaRminimization. These concepts are taken into consideration to propose representations and solution methods for the above class of SSD based models.We describe a cutting plane based solution algorithm and outline implementation details. A computational study is presented, which demonstrates the effectiveness and the scale-up properties of the solution algorithm, as applied to the SSD model of Roman et al. (Math Program, Ser B 108:541569, 2006).
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Asset-Liability Management & Liability Driven Investment
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Supply Chain Management
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News Analytics and Sentiment Analysis
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Scenario Generation
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In this project we analyze the FTSE 100 and the Euro Stoxx 50 data series via the well-known Hidden Markov Model (HMM). Using this model, we are able to better capture the stylized factors such as fat tails and volatility clustering compared with the Geometric Brownian motion (GBM), and find the market signal to forecast the future market conditions.
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Quadratic Programming
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Solution Algorithm
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Residual Risk Model
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Commodity Spreads
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