scholarly journals A Semi-Markov Leaky Integrate-and-Fire Model

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1022
Author(s):  
Giacomo Ascione ◽  
Bruno Toaldo
Keyword(s):  
Markov Process ◽  
Waiting Times ◽  
Markov Property ◽  
Fire Model ◽  
Integrate And Fire ◽  
Heavy Tailed Distribution ◽  
Semi Markov Process ◽  
The Mean ◽  
Heavy Tailed ◽  
Mean Variance

In this paper, a Leaky Integrate-and-Fire (LIF) model for the membrane potential of a neuron is considered, in case the potential process is a semi-Markov process. Semi-Markov property is obtained here by means of the time-change of a Gauss-Markov process. This model has some merits, including heavy-tailed distribution of the waiting times between spikes. This and other properties of the process, such as the mean, variance and autocovariance, are discussed.

scholarly journals A Bias-Reduced Estimator for the Mean of a Heavy-Tailed Distribution with an Infinite Second Moment

2012 ◽  
Author(s):  
Brahim Brahimi ◽  
Djamel Meraghni ◽  
Necir Abdelhakim ◽  
Yahia Djabrane
Keyword(s):  
Second Moment ◽  
Heavy Tailed Distribution ◽  
The Mean ◽  
Heavy Tailed

scholarly journals A bias-reduced estimator for the mean of a heavy-tailed distribution with an infinite second moment

2013 ◽  
Vol 143 (6) ◽  
pp. 1064-1081 ◽  
Author(s):  
Brahim Brahimi ◽  
Djamel Meraghni ◽  
Abdelhakim Necir ◽  
Djabrane Yahia
Keyword(s):  
Second Moment ◽  
Heavy Tailed Distribution ◽  
The Mean ◽  
Heavy Tailed

Markowitz Theory in Portfolio Optimization for Heavy Tailed Assets

2019 ◽  
Vol 1 (3) ◽  
pp. 1-14
Author(s):  
Wong Ghee Ching ◽  
Che Mohd Imran Che Taib
Keyword(s):  
Portfolio Optimization ◽  
Composite Index ◽  
Minimum Variance ◽  
Optimization Techniques ◽  
Expected Return ◽  
Markowitz Model ◽  
The Mean ◽  
Heavy Tailed ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper aims at solving an optimization problem in the presence of heavy tail behavior of financial assets. The question of minimizing risk subjected to a certain expected return or maximizing return for a given expected risk are two objective functions to be solved using Markowitz model. The Markowitz based strategies namely the mean variance portfolio, minimum variance portfolio and equally weighted portfolio are proposed in conjunction with mean and variance analysis of the portfolio. The historical prices of stocks traded at Bursa Malaysia are used for empirical analysis. We employed CAPM in order to investigate the performance of the Markowitz model which was benchmarked with risk adjusted KLSE Composite Index. We performed a backtesting study of portfolio optimization techniques defined under modern portfolio theory in order to find the optimal portfolio. Our findings showed that the mean variance portfolio outperformed the other two strategies in terms of performance of investment for heavy tailed assets.

Markov regenerative credit rating model

2017 ◽  
Vol 18 (3) ◽  
pp. 311-325 ◽  
Author(s):  
Puneet Pasricha ◽  
Dharmaraja Selvamuthu ◽  
Viswanathan Arunachalam
Keyword(s):  
Markov Process ◽  
Credit Rating ◽  
Markov Property ◽  
Regenerative Process ◽  
Rating Data ◽  
Content Type ◽  
Proposed Model ◽  
Semi Markov Process ◽  
Probability Matrices ◽  
Rating Changes

Purpose Credit ratings serve as an important input in several applications in risk management of the financial firms. The level of credit rating changes from time to time because of random credit risk and, thus, can be modeled by an appropriate stochastic process. Markov chain models have been widely used in the literature to generate credit migration matrices; however, emergent empirical evidences suggest that the Markov property is not appropriate for credit rating dynamics. The purpose of this article is to address the non-Markov behavior of the rating dynamics. Design/methodology/approach This paper proposes a model based on Markov regenerative process (MRGP) with subordinated semi-Markov process (SMP) to obtain the estimates of rating migration probability matrices and default probabilities. Numerical example is given to illustrate the applicability of the proposed model with the help of historical Standard & Poor’s (S&P) credit rating data. Findings The proposed model implies that rating of a firm in the future not only depends on its present rating, but also on its previous ratings. If a firm gets a rating lower than its previous ratings, there are higher chances of further downgrades, and the issue is called the rating momentum. The model also addresses the ageing problem of credit rating evolution. Originality/value The contribution of this paper is a more general approach to study the rating dynamics and overcome the issues of inappropriateness of Markov process applied in rating dynamics.

scholarly journals How Sample Paths of Leaky Integrate-and-Fire Models Are Influenced by the Presence of a Firing Threshold

2011 ◽  
Vol 23 (7) ◽  
pp. 1743-1767 ◽  
Author(s):  
Maria Teresa Giraudo ◽  
Priscilla E. Greenwood ◽  
Laura Sacerdote
Keyword(s):  
Membrane Potential ◽  
Diffusion Process ◽  
Fixed Time ◽  
Firing Time ◽  
Fire Model ◽  
Integrate And Fire ◽  
Sample Paths ◽  
The Mean ◽  
First Time

Neural membrane potential data are necessarily conditional on observation being prior to a firing time. In a stochastic leaky integrate-and-fire model, this corresponds to conditioning the process on not crossing a boundary. In the literature, simulation and estimation have almost always been done using unconditioned processes. In this letter, we determine the stochastic differential equations of a diffusion process conditioned to stay below a level S up to a fixed time t1 and of a diffusion process conditioned to cross the boundary for the first time at t1. This allows simulation of sample paths and identification of the corresponding mean process. Differences between the mean of free and conditioned processes are illustrated, as well as the role of noise in increasing these differences.

scholarly journals Estimating the Mean of Heavy-tailed Distribution under Random Truncation

2021 ◽  
pp. 273-286
Author(s):  
Ben Dahmane Khanssa
Keyword(s):  
Asymptotic Normality ◽  
Simulation Study ◽  
Random Variable ◽  
Finite Sample ◽  
Heavy Tailed Distribution ◽  
The Mean ◽  
Heavy Tailed ◽  
Alternative Estimator ◽  
The Right ◽  
Random Truncation

Inspired by L.Peng’s work on estimating the mean of heavy-tailed distribution in the case of completed data. we propose an alternative estimator and study its asymptotic normality when it comes to the right truncated random variable. A simulation study is executed to evaluate the finite sample behavior on the proposed estimator

scholarly journals Estimating the Mean Cover Time of a Semi-Markov Process via Simulation

1997 ◽  
Vol 11 (2) ◽  
pp. 267-271 ◽  
Author(s):  
Erol Peköz ◽  
Sheldon M. Ross
Keyword(s):  
Markov Process ◽  
Cover Time ◽  
Expected Time ◽  
Efficient Simulation ◽  
Finite State ◽  
Semi Markov Process ◽  
The Mean

An efficient simulation estimator of the expected time until all states of a finite state semi-Markov process have been visited is determined.

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