Some insights into the solution algorithms for SLP problems

We consider classes of stochastic linear programming problems which can be efficiently solved by deterministic algorithms. For two-stage recourse problems we identify two such classes. The first one consists of problems where the number of stochastically independent random variables is relatively low; the second class is the class of simple recourse problems. The proposed deterministic algorithm is successive discrete approximation. We also illustrate the impact of required accuracy on the efficiency of this algorithm. For jointly chance constrained problems with a random right-hand-side and multivariate normal distribution we demonstrate the increase in efficiency when lower accuracy is required, for a central cutting plane method. We support our argumentation and findings with computational result

Computational aspects of minimizing conditional value-at-risk

Abstract.: We consider optimization problems for minimizing conditional value-at-risk (CVaR) from a computational point of view, with an emphasis on financial applications. As a general solution approach, we suggest to reformulate these CVaR optimization problems as two-stage recourse problems of stochastic programming. Specializing the L-shaped method leads to a new algorithm for minimizing conditional value-at-risk. We implemented the algorithm as the solver CVaRMin. For illustrating the performance of this algorithm, we present some comparative computational results with two kinds of test problems. Firstly, we consider portfolio optimization problems with 5 random variables. Such problems involving conditional value at risk play an important role in financial risk management. Therefore, besides testing the performance of the proposed algorithm, we also present computational results of interest in finance. Secondly, with the explicit aim of testing algorithm performance, we also present comparative computational results with randomly generated test problems involving 50 random variables. In all our tests, the experimental solver, based on the new approach, outperformed by at least one order of magnitude all general-purpose solvers, with an accuracy of solution being in the same range as that with the LP solver

Computational aspects of prospect theory with asset pricing applications

We develop an algorithm to compute assetallocations for Kahneman and Tversky's (Econometrica, 47(2), 263-291, 1979) prospect theory. An application to benchmark data as in Fama and French (Journal of Financial Economics, 47(2), 427-465, 1992) shows that the equity premium puzzle is resolved for parameter values similar to those found in the laboratory experiments of Kahneman and Tversky (Econometrica, 47(2), 263-291, 1979). While previous studies like Benartzi and Thaler (The Quarterly Journal of Economics, 110(1), 73-92, 1995), Barberis, Huang and Santos (The Quarterly Journal of Economics, 116(1), 1-53, 2001), and Grüne and Semmler (Asset prices and loss aversion, Germany, Mimeo Bielefeld University, 2005) focussed on dynamic aspects of asset pricing but only used loss aversion to explain the equity premium puzzle our paper explains the unconditional moments of asset pricing by a static two-period optimization problem. However, we incorporate asymmetric risk aversion. Our approach allows reducing the degree of loss aversion from 2.353 to 2.25, which is the value found by Tversky and Kahneman (Journal of Risk and Uncertainty, 5, 297-323, 1992) while increasing the risk aversion from 1 to 0.894, which is a slightly higher value than the 0.88 found by Tversky and Kahneman (Journal of Risk and Uncertainty, 5, 297-323, 1992). The equivalence of these parameter settings is robust to incorporating the size and the value portfolios of Fama and French (Journal of Finance, 47(2), 427-465, 1992). However, the optimal prospect theory portfolios found on this larger set of assets differ drastically from the optimal mean-variance portfoli

Cumulative prospect theory and mean-variance analysis: a rigorous comparison

We propose a numerical optimization approach that can be used to solve portfolio selection problems including several assets and involving objective functions from cumulative prospect theory (CPT). Implementing the suggested algorithm, we compare asset allocations that are derived for CPT based on two different methods: maximizing CPT along the mean–variance efficient frontier so that simple mean–variance algorithms can be used, and maximizing CPT without this restriction. According to the theoretical literature, with normally distributed returns and unlimited short sales, these two approaches lead to the same optimal solutions. We find that for empirical finite discrete distributions obtained via sampling and subsequent clustering from a normal distribution, the difference between the two approaches remains negligible even if short sales are restricted. However, if standard asset allocation data for pension funds is considered, the difference is considerable. Moreover, for certain types of derivatives, such as call options, the restriction of asset allocations to the mean–variance efficient frontier produces sizable losses in various respects, including decreases in expected returns and expected utility. We are able to explain these differences by CPT’s preference for positive skewness, which is not accounted for by optimizing CPT along the mean–variance efficient frontier

Irodalmi kommunikáció és értékrend (A görög értékrend alakulása különös tekintettel a hellenisztikus korra. A római mos maiorum az Augustus-kortól a patrisztikus korig.) = Literary communication and system of values. (The formation of Greek values especially in the Hellenistic Age. The Roman mos maiorum from the age of Augustus until the patristic age.)

Az irodalmi értékrend és kommunikáció kérdését a pályázatban résztvevők a következő irodalmi korszakokban vizsgálták: a./ korai görög líra - iambos, kitekintéssel a hellenisztikus korra és a római lírára, valamint a humanista latin nyelvű irodalomra. Az iambos mint a értékrend kifejezésre juttatója. b./ római aranykor - értékfogalmak Cicero Partitionesében. Vergilius, Horatius, Ovidius művei és az Augustusi propaganda; utóbbi más médiumokban (ikonográfia, numizmatika) való kifejeződése. c./ császárkori epika - a középpontban Lucanusszal. A korábbi értékrendhez való viszony. d./ kései császárkor - a vegyesházasságok kapcsán a házassággal kapcsolatos fogalmak helye a pogány és keresztény értékrendben. Az antiszemitizmus kérdése a CTh 3,7,2 vizsgálata alapján. Eredmény: 46 tétel (disszertációk, tanulmányok, adatbázisok, előadások) | The problem of the literary scale of values and that of literary communication has been examined in the following literary periods: a./ early Greek iambos, with outlook to the hellenistic period, to the Latin poetry and to the humanistic Latin literature. Tha iambos as expression of the scale of values. b./ Roman golden age - concept of values in the Partitiones by Cicero. The works of Vergile, Horace and Ovid and the Augustan propaganda; expression of the augustan propaganda in other media (iconography, numismatics). c./ Roman epics of the 1. c. A.D. - in the centre with Lucan. Relation of values to the earlier value-system. d./ later imperial centuries - part of the ideas connected with the matrimony with reference to the mixed matrimonies in the pagan and Christian scale of values. The problem of antisemitism on examination of CTh 3,72. Results: 46 theses (dissertations, essays, databases, papers

Pairing Ensemble Numerical Weather Prediction with Ensemble Physical Model Chain for Probabilistic Photovoltaic Power Forecasting

Under the two-step framework of photovoltaic (PV) power forecasting, that is, forecasting first the irradiance and then converting it to PV power, there are two chief ways in which one can account for the uncertainty embedded in the final PV power forecast. One of those is to produce probabilistic irradiance forecast through, for example, ensemble numerical weather prediction (NWP), and the other is to pass the irradiance forecast through a collection of different irradiance-to-power conversion sequences, which are known as model chains. This work investigates, for the first time, into the question: Whether pairing ensemble NWP with ensemble model chain is better than leveraging any individual method alone? Using data from 14 utility-scale ground-mounted PV plants in Hungary and the state-of-the-art global mesoscale NWP model of the European Centre for Medium-Range Weather Forecasts, it is herein demonstrated that the best probabilistic PV power forecast needs to consider both ensemble NWP and ensemble model chain. Furthermore, owing to the higher-quality probabilistic forecasts, the point forecast accuracy is also improved substantially through pairing. Overall, the recommended paring strategy achieves a mean-normalized continuous ranked probability score and a root mean square error of 18.4% and 42.1%, respectively