New Economics Papers
on Computational Economics
Issue of 2010‒09‒03
eight papers chosen by

  1. A comparative study of the Lasso-type and heuristic model selection methods By Ivan Savin
  2. Belief Propagation Algorithm for Portfolio Optimization Problems By Takashi Shinzato; Muneki Yasuda
  3. Solving the Multi-Country Real Business Cycle Model Using Ergodic Set Methods By Serguei Maliar; Lilia Maliar; Kenneth L. Judd
  4. Simple simulation of diffusion bridges with application to likelihood inference for diffusions By Mogens Bladt; Michael Sørensen
  5. ErbSiHM 0.1 By Houben, Henriette; Maiterth, Ralf
  6. Picard Approximation of Stochastic Differential Equations and Application to Libor Models By Antonis Papapantoleon; David Skovmand
  7. Simulation of Diversified Portfolios in a Continuous Financial Market By Eckhard Platen; Renata Rendek
  8. Monte Carlo Portfolio Optimization for General Investor Risk-Return Objectives and Arbitrary Return Distributions: a Solution for Long-only Portfolios By William T. Shaw

  1. By: Ivan Savin
    Abstract: This study presents a first comparative analysis of Lasso-type (Lasso, adaptive Lasso, elastic net) and heuristic subset selection methods. Although the Lasso has shown success in many situations, it has some limitations. In particular, inconsistent results are obtained for pairwise strongly correlated predictors. An alternative to the Lasso is constituted by model selection based on information criteria (IC), which remains consistent in the situation mentioned. However, these criteria are hard to optimize due to a discrete search space. To overcome this problem, an optimization heuristic (Genetic Algorithm) is applied. Monte-Carlo simulation results are reported to illustrate the performance of the methods.
    Keywords: Model selection, Lasso, adaptive Lasso, elastic net, heuristic methods, genetic algorithms
    Date: 2010–08–24
  2. By: Takashi Shinzato; Muneki Yasuda
    Abstract: The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti and M. M\'ezard [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.
    Date: 2010–08
  3. By: Serguei Maliar; Lilia Maliar; Kenneth L. Judd
    Abstract: We use the stochastic simulation algorithm, described in Judd, Maliar and Maliar (2009), and the cluster-grid algorithm, developed in Judd, Maliar and Maliar (2010a), to solve a collection of multi-country real business cycle models. The following ingredients help us reduce the cost in high-dimensional problems: an endogenous grid enclosing the ergodic set, linear approximation methods, fixed-point iteration and efficient integration methods, such as non-product monomial rules and Monte Carlo integration combined with regression. We show that high accuracy in intratemporal choice is crucial for the overall accuracy of solutions and offer two approaches, precomputation and iteration-on-allocation, that can solve for intratemporal choice both accurately and quickly. We also implement a hybrid solution algorithm that combines the perturbation and accurate intratemporal-choice methods.
    JEL: C63 C68
    Date: 2010–08
  4. By: Mogens Bladt (Universidad Nacional Autónoma de México); Michael Sørensen (University of Copenhagen and CREATES)
    Abstract: With a view to likelihood inference for discretely observed diffusion type models, we propose a simple method of simulating approximations to diffusion bridges. The method is applicable to all one-dimensional diffusion processes and has the advantage that simple simulation methods like the Euler scheme can be applied to bridge simulation. Another advantage over other bridge simulation methods is that the proposed method works well when the diffusion bridge is defined in a long interval because the computational complexity of the method is linear in the length of the interval. In a simulation study we investigate the accuracy and efficiency of the new method and compare it to exact simulation methods. In the study the method provides a very good approximation to the distribution of a diffusion bridge for bridges that are likely to occur in applications to likelihood inference. To illustrate the usefulness of the new method, we present an EM-algorithm for a discretely observed diffusion process. We demonstrate how this estimation method simplifies for exponential families of diffusions and very briefly consider Bayesian inference.
    Keywords: Bayesian inference, diffusion bridge, discretely sampled diffusions, EM-algorithm, Euler scheme, likelihood inference, time-reversion
    JEL: C22 C15
    Date: 2010–08–05
  5. By: Houben, Henriette; Maiterth, Ralf
    Abstract: This contribution describes ErbSiHM 0.1 which is an inheritance tax simulation model. ErbSiHM 0.1 comprises of a microsimulation model based on the data of the German Inheritance Tax Statistics 2002 and a group simulation model employing the data of the SOEP. The microsimulation model of ErbSiHM 0.1 allows for detailed analyses of revenue and distributional effects of the German inheritance tax or inheritance tax reform proposals. In addition the impact of the inheritance tax on the tax burden of particular groups of taxpayers can be detected. As the German Inheritance Tax Statistics do not include data of transfers of low-value estates a supplementary group model based on the data of the SOEP has been designed. This SOEP-based supplementary model is in particular useful to estimate revenue effects of tax reforms. --
    Date: 2010
  6. By: Antonis Papapantoleon (Institute of Mathematics, TU Berlin and Quantitative Products Laboratory, Deutsche Bank AG); David Skovmand (Aarhus School of Business and CREATES)
    Abstract: The aim of this work is to provide fast and accurate approx- imation schemes for the Monte Carlo pricing of derivatives in LIBOR market models. Standard methods can be applied to solve the stochas- tic differential equations of the successive LIBOR rates but the methods are generally slow. Our contribution is twofold. Firstly, we propose an alternative approximation scheme based on Picard iterations. This ap- proach is similar in accuracy to the Euler discretization, but with the feature that each rate is evolved independently of the other rates in the term structure. This enables simultaneous calculation of derivative prices of different maturities using parallel computing. Secondly, the product terms occurring in the drift of a LIBOR market model driven by a jump process grow exponentially as a function of the number of rates, quickly rendering the model intractable. We reduce this growth from exponen- tial to quadratic using truncated expansions of the product terms. We include numerical illustrations of the accuracy and speed of our method pricing caplets, swaptions and forward rate agreements.
    Keywords: LIBOR models, Lévy processes, Picard approximation, drift expansion, parallel computing.
    JEL: G12 G13 C63
    Date: 2010–07–16
  7. By: Eckhard Platen (School of Finance and Economics, University of Technology, Sydney); Renata Rendek (School of Finance and Economics, University of Technology, Sydney)
    Abstract: The paper analyzes the simulated long-term behavior of well diversi?ed portfolios in continuous financial markets. It focuses on the equi-weighted index and the market portfolio. The paper illustrates that the equally weighted portfolio constitutes a good proxy of the growth optimal portfolio, which maximizes expected logarithmic utility. The multi-asset market models considered include the Black-Scholes model, the Heston model, the ARCH diffusion model, the geometric Ornstein-Uhlenbeck volatility model and a multi-asset version of the minimal market model. All these models are simulated exactly or almost exactly over an extremely long period of time to analyze the long term growth of the respective portfolios. The paper illustrates the robustness of the diversification phenomenon when approximating the growth optimal portfolio by the equi-weighted index. Significant outperformance in the long run of the market capitalization weighted portfolio by the equi-weighted index is documented for different market models. Under the multi-asset minimal market model the equi-weighted index outperforms remarkably the market portfolio. In this case the benchmarked market portfolio is a strict supermartingale, whereas the benchmarked equi-weighted index is a martingale. Equal value weighting overcomes the strict supermartingale property that the benchmarked market portfolio inherits from its strict supermartingale constituents under this model.
    Keywords: Growth optimal portfolio; Diversi?cation Theorem; diversi?ed portfolios; market portfolio; equi-weighted index; almost exact simulation; minimal market model
    Date: 2010–08–01
  8. By: William T. Shaw
    Abstract: We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random portfolios may be generated. A practical scheme for the long-only fully-invested problem is developed and tested for the classic QP application. The advantage of Monte Carlo methods is that they may be extended to risk functions that are more complicated functions of the return distribution, and that the underlying return distribution may be computed without the classical Gaussian limitations. The optimization of quadratic risk-return functions, VaR, CVaR, may be handled in a similar manner to variability ratios such as Sortino and Omega, or mathematical constructions such as expected utility and its behavioural finance extensions. Robustification is also possible. Grid computing technology is an excellent platform for the development of such computations due to the intrinsically parallel nature of the computation, coupled to the requirement to transmit only small packets of data over the grid. We give some examples deploying GridMathematica, in which various investor risk preferences are optimized with differing multivariate distributions. Good comparisons with established results in Mean-Variance and CVaR optimization are obtained when ``edge-vertex-biased'' sampling methods are employed to create random portfolios. We also give an application to Omega optimization.
    Date: 2010–08

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