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On the tracking and replication of hedge fund optimal investment portfolio strategies in global capital markets in presence of nonlinearities, applying Bayesian filters: 1. Stratanovich – Kalman – Bucy filters for Gaussian linear investment returns distribution and 2. Particle filters for non-Gaussian non-linear investment returns distribution

Author

Listed:
  • Ledenyov, Dimitri O.
  • Ledenyov, Viktor O.

Abstract

The hedge fund represents a unique investment opportunity for the institutional and private investors in the diffusion-type financial systems. The main objective of this condensed article is to research the hedge fund’s optimal investment portfolio strategies selection in the global capital markets with the nonlinearities. We provide a definition for the hedge fund, describe the hedge fund’s organization structures and characteristics, discuss the hedge fund’s optimal investment portfolio strategies and review the appropriate hedge fund’s risk assessment models for investing in the global capital markets in time of high volatilities. We analyze the advanced techniques for the hedge fund’s optimal investment portfolio strategies replication, based on both the Stratonovich – Kalman - Bucy filtering algorithm and the particle filtering algorithm. We developed the software program with the embedded Stratonovich – Kalman - Bucy filtering algorithm and the particle filtering algorithm, aiming to track and replicate the hedge funds optimal investment portfolio strategies in the practical cases of the non-Gaussian non-linear chaotic distributions.

Suggested Citation

  • Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "On the tracking and replication of hedge fund optimal investment portfolio strategies in global capital markets in presence of nonlinearities, applying Bayesian filters: 1. Stratanovich – Kalman – Buc," MPRA Paper 51046, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:51046
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    File URL: https://mpra.ub.uni-muenchen.de/51176/8/MPRA_paper_51176.pdf
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    References listed on IDEAS

    as
    1. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    2. Friedman, Moshe & Harris, Lawrence, 1998. "A Maximum Likelihood Approach for Non-Gaussian Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 284-291, July.
    3. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
    4. Rabe-Hesketh, Sophia & Skrondal, Anders & Pickles, Andrew, 2005. "Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects," Journal of Econometrics, Elsevier, vol. 128(2), pages 301-323, October.
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    7. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2002. "Reliable estimation of generalized linear mixed models using adaptive quadrature," Stata Journal, StataCorp LP, vol. 2(1), pages 1-21, February.
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    10. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
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    More about this item

    Keywords

    hedge fund; investment portfolio; investment strategy; global tactical asset allocation investment strategy; investment decision making; return on investments; value at risk; arbitrage pricing theory; Sharpe ratio; separation theorem; Sortino ratio; Sterling ratio; Calmar ratio; Gini coefficient; value at risk (VaR); Ledenyov investment portfolio theorem; stability of investment portfolio; Kolmogorov chaos theory; Sharkovsky chaos theory; Lyapunov stability criteria; bifurcation diagram; nonlinearities; stochastic volatility; stochastic probability; Markov chain; Bayesian estimation; Bayesian filters; Wiener filtering theory; Stratonovich optimal non-linear filtering theory; Stratonovich – Kalman – Bucy filtering algorithm; Hodrick-Prescott filter; Hirose - Kamada filter; particle filtering methods; particle filters; multivariate filters; Gaussian linear distribution; non-Gaussian nonlinear distribution; Monte-Carlo simulation; Brownian motion; diffusion process; econophysics; econometrics; global capital markets.;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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