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

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 StratonovichKalman -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 nonGaussian non-linear chaotic distributions. JEL: G00, G01, G11, G12, G 20, G23, C10, C58, C60 ; LCC: HF 4001-4280.7, HF 5681.H43 ; PACS numbers: 89.65. Gh, 89.75.Fb .