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Pricing dynamic fund protection under hidden Markov models

IMA JOURNAL OF MANAGEMENT MATHEMATICS 2018年第1期29卷 99-117页

作者： Fan, Kun Shen, Yang Siu, Tak Kuen Wang, Rongming East China Normal Univ Sch Stat Shanghai 200241 Peoples R China York Univ Dept Math & Stat Toronto ON M3J 1P3 Canada Macquarie Univ Fac Business & Econ Dept Appl Finance & Actuarial Studies Sydney NSW 2109 Australia

In this article, we discuss the pricing of dynamic fund protection when the value process of the investment fund is governed by a geometric Brownian motion with parameters modulated by a continuous-time, finite-state hidden Markov chain. Under a risk-neutral probability measure, selected by the Esscher transform, we adopt the partial differential equation approach to value the dynamic fund protection. Using the estimated sequence of the hidden Markov chain, we apply the baum-welch algorithm and the Viterbi algorithm to derive the maximum likelihood estimates of the parameters. Numerical examples are provided to illustrate the practical implementation of the model.

关键词： dynamic fund protection hidden Markov model baum-welch algorithm Viterbi algorithm

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Concatenation of space-time block codes and turbo trellis coded modulation (ST-TTCM) over Rician fading channels with imperfect phase

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INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS 2004年第4期17卷 347-361页

作者： Ucan, ON Osman, O Univ Istanbul Fac Engn Dept Elect TR-34850 Istanbul Turkey Istanbul Commerce Univ TR-34378 Istanbul Turkey

In this paper, the performance of space time-turbo trellis coded modulation (ST-TTCM) is evaluated over Rician and Rayleigh fading channels with imperfect phase. We modify baum-welch (BW) algorithm to estimate the fading and phase jitter parameters for multi-antenna configurations. Thus, we assume that the channel parameters change slower than carrier frequency. We know that, at high data rate transmissions over wireless fading channels, space-time block codes (STBC) provide the maximal possible diversity advantage. Here, the combined effects of the amplitude and the phase of the received signal are considered, each one modelled by Rician and Tikhonov distributions, respectively. We investigate space time-turbo trellis coded modulation (ST-TTCM) for 8-PSK for several Rician factor K and phase distortion factor eta. Thus. our results reflect the degradations both due to the effects of the fading on the amplitude and phase noise of the received signal while the channel parameters are estimated by BW algorithm. Copyright (C) 2004 John Wiley Sons, Ltd.

关键词： space time-turbo trellis coded modulation channel estimation baum-welch algorithm Rician channel phase jitter

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Additive and Nonadditive Fuzzy Hidden Markov Models

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2010年第1期18卷 40-56页

作者： Verma, Nishchal K. Hanmandlu, M. Indian Inst Technol Dept Elect Engn Kanpur 208016 Uttar Pradesh India Indian Inst Technol Dept Elect Engn New Delhi 110016 India

We present a novel approach for the development of fuzzy hidden Markov models (FHMMs) by exploiting both additive and nonadditive properties of input fuzzy sets in the fuzzy rules of generalized fuzzy model (GFM). This development utilizes 1) Gaussian mixture model (GMM) to manipulate the mixture parameters for the input fuzzy sets and 2) GFM rules for the inclusion of states in the consequent part to be able to use HMM. Taking the components of Gaussian mixture density conditioned on the past system states and making use of equivalence of GMM with GFM, parameters of the additive and nonadditive FHMMs are estimated using the forward-backward procedure of the baum-welch algorithm. The additive and nonadditive FHMMs are validated on three benchmark applications involving time-series prediction, and the results are compared and found to be better than or equal to those of the existing recent fuzzy models.

关键词： Additive and nonadditive fuzzy systems baum-welch algorithm Choquet fuzzy integral Gaussian mixture model (GMM) generalized fuzzy model (GFM) hidden Markov model (HMM) Q-measure

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GA Optimized HMM Error Model for OFDM

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WIRELESS PERSONAL COMMUNICATIONS 2017年第1期96卷 621-633页

作者： Ranjan, Rakesh Mitra, Debjani Natl Inst Technol Dept Elect & Commun Engn Patna Bihar India Indian Sch Mines Indian Inst Technol Dept Elect Engn Dhanbad Bihar India

Finite-state HMM error models are an established powerful tool for capturing temporal characteristics of fading channels. They make network simulations much more practical and fast while developing and testing higher layer wireless system protocols and designing interleaving and FEC schemes. This paper has introduced two new Genetic algorithm (GA) based approaches, namely, GA-S and GA-B as an alternative to HMM error models, for the accurate learning of error statistics of autocorrelation function (ACF) and error-run distributions. Validity comparisons of fit obtained show that the GA method is better than both the conventional baum-welch algorithm (BWA) and Semi-hidden Markov model (SHMM) methods, even when the target sequences are as short as 1000 in length. The independent elements of the [A] and [B] parameters of BWA used as chromosomes of the population space are used for error generation within the Genetic algorithm. Mean square error of statistical properties of the error sequences is used to determine fitness of the chromosomes unlike other works using average log-likelihood ratio. Applicability has been tested by numerical simulations using error sequences of different lengths as well as target sequences of fixed length from an OFDM transceiver system under different fading rates. A T (s) spaced time-delay model of the propagation channel with a fixed power delay profile has been used. For slow faded channels or when long sequences of error free intervals poses difficulties for BWA training, the GA method proves to be an excellent alternative for fast and accurate modeling of the error bursts. Unlike the computationally cumbersome BWA or the simplified SHMM approach, the GA model is capable of arriving at desired levels of accuracy with two to three states, in contrast to the Markov models needing a much higher number of states.

关键词： Genetic algorithm baum-welch algorithm Hidden Markov model Autocorrelation function OFDM Fading

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Combined turbo detection and decoding for unknown ISI channels

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IEEE TRANSACTIONS ON COMMUNICATIONS 2003年第1期51卷 79-85页

作者： Garcia-Frias, J Villasenor, JD Univ Delaware Dept Elect & Comp Engn Newark DE 19716 USA Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90024 USA

We present two decoding structures which combine turbo detection and decoding, allowing communication in the presence of intersymbol interference (ISI). The first one treats the ISI as another constituent decoder which participates in the exchange of extrinsic information, and performs slightly worse than the second structure, which combines the trellis representing each one of the constituent encoders with the ISI trellis. We show that for both methods, it is possible to obtain good performance, even when no a priori information about the ISI channel is available to the decoder.

关键词： baum-welch algorithm intersymbol interference (ISI) channels iterative decoding joint parameter estimation and decoding turbo codes

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Turbo decoding of Gilbert-Elliot channels

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IEEE TRANSACTIONS ON COMMUNICATIONS 2002年第3期50卷 357-363页

作者： Garcia-Frias, J Villasenor, JD Univ Delaware Dept Elect & Comp Engn Newark DE 19716 USA Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90024 USA

We describe parallel concatenated codes for communication over finite-state binary Markov channels. We present encoder design techniques and decoder processing modifications that utilize the a priori statistics of the channel and show that the resulting codes allow reliable communication at rates which are above the capacity of a memoryless channel with the same stationary bit error probability as the Markov channel. These codes outperform systems based on the traditional approach of using a channel interleaver to create a channel which is assumed to be memoryless. In addition, we introduce a joint estimation/decoding method that allows the estimation of the parameters of the hidden Markov model when they are not known a priori.

关键词： baum-welch algorithm finite-state binary Markov channels Gilbert-Elliot channels iterative decoding turbo codes

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Low complexity generalized EM algorithm for blind channel estimation and data detection in optical communication systems

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SIGNAL PROCESSING 2006年第11期86卷 3393-3403页

作者： Lisnanski, Roman Weiss, Anthony J. Tel Aviv Univ Dept Elect Engn Syst IL-69978 Tel Aviv Israel

Expectation-Maximization algorithm (EM) has been used in the past for blind estimation of intersymbol interference channels characterized by additive white Gaussian noise. When the channel is characterized by non-Gaussian, signal-dependent noise, the computational complexity of direct application of EM becomes prohibitively high. In this paper, a low complexity generalized EM algorithm is presented. The proposed algorithm achieves a major reduction in computational complexity compared to the EM algorithm and can be applied to nonlinear finite memory channels with non-Gaussian signal-dependent noise. Simulation results are presented for intensity modulated direct detection optical channel that is characterized by non-central chi-square distribution noise. (c) 2006 Elsevier B.V. All rights reserved.

关键词： blind channel estimation non-gaussian signal-dependent noise non-central chi-square noise maximum likelihood generalized EM hidden Markov models baum-welch algorithm

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Comparing and evaluating HMM ensemble training algorithms using train and test and condition number criteria

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PATTERN ANALYSIS AND APPLICATIONS 2003年第4期6卷 327-336页

作者： Davis, RIA Lovell, BC Univ Queensland Sch Informat Technol & Elect Engn Intelligent Real Time Imaging & Sensing Grp Brisbane Qld 4072 Australia

Hidden Markov Models have many applications in signal processing and pattern recognition, but their convergence-based training algorithms are known to suffer from over-sensitivity to the initial random model choice. This paper describes the boundary between regions in which ensemble learning is superior to Rabiner's multiple-sequence baum-welch training method, and proposes techniques for determining the best method in any arbitrary situation. It also studies the suitability of the training methods using the condition number, a recently proposed diagnostic tool for testing the quality of the model. A new method for training Hidden Markov Models called the Viterbi Path Counting algorithm is introduced and is found to produce significantly better performance than current methods in a range of trials.

关键词： baum-welch algorithm ensemble learning hidden Markov model model structure multiple sequence Viterbi

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The influence of initial conditions on maximum likelihood estimation of the parameters of a binary hidden Markov model

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STATISTICS & PROBABILITY LETTERS 1998年第1期40卷 67-73页

作者： Dunmur, AP Titterington, DM Univ Glasgow Dept Stat Glasgow G12 8QW Lanark Scotland

The baum-welch (EM) algorithm is a familiar tool for calculation of the maximum likelihood estimate of the parameters in hidden Markov chain models. For the particular case of a binary Markov chain corrupted by binary channel noise a detailed study is carried out of the influence that the initial conditions impose on the results produced by the algorithm. (C) 1998 Elsevier Science B.V. All rights reserved.

关键词： baum-welch algorithm binary Markov chain EM algorithm initial conditions

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An autoregressive model to describe fishing vessel movement and activity

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ENVIRONMETRICS 2015年第1期26卷 17-28页

作者： Gloaguen, P. Mahevas, S. Rivot, E. Woillez, M. Guitton, J. Vermard, Y. Etienne, M. P. IFREMER F-44311 Nantes 03 France AGROCAMPUS OUEST UMR Ecol & St Ecosyst 985 CS84215 F-35042 Rennes France IFREMER F-29280 Plouzane France IFREMER Channel & North Sea Fisheries Dept F-62321 Boulogne Sur Mer France AGROPARISTECH UMR MIA 518 F-75231 Paris France

The understanding of the dynamics of fishing vessels is of great interest to characterize the spatial distribution of the fishing effort and to define sustainable fishing strategies. It is also a prerequisite for anticipating changes in fishermen's activity in reaction to management rules, economic context, or evolution of exploited resources. Analyzing the trajectories of individual vessels offers promising perspectives to describe the activity during fishing trips. A hidden Markov model with two behavioral states (steaming and fishing) is developed to infer the sequence of non-observed fishing vessel behavior along the vessel trajectory based on Global Positioning System (GPS) records. Conditionally to the behavior, vessel velocity is modeled with an autoregressive process. The model parameters and the sequence of hidden behavioral states are estimated using an expectation-maximization algorithm, coupled with the Viterbi algorithm that captures the most credible joint sequence of hidden states. A simulation approach was performed to assess the influence of contrast between the model parameters and of the path length on the estimation performances. The model was then fitted to four original GPS tracks recorded with a time step of 15min derived from volunteer fishing vessels operating in the Channel within the IFREMER RECOPESCA project. Results showed that the fishing activity performed influenced the estimates of the velocity process parameters. Results also suggested future inclusion of variables such as tide currents within the ecosystem approach of fisheries. Copyright (c) 2014 John Wiley & Sons, Ltd.

关键词： hidden Markov model vessels dynamics RECOPESCA autoregressive process baum-welch algorithm

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