1,721,101 research outputs found

    The application of continuous-time random walks in finance and economics

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    This paper reviews some applications of continuous time random walks (CTRWs) to Finance and Economics. It is divided into two parts. The first part deals with the connection between CTRWs and anomalous diffusion. In particular, a simplified version of the well-scaled transition of CTRWs to the diffusive or hydrodynamic limit is presented. In the second part, applications of CTRWs to the ruin theory of insurance companies, to growth and inequality processes and to the dynamics of prices in financial markets are outlined and briefly discussed

    Scaling in the market of futures

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    The price time series of the Italian government bonds (BTP) futures is studied by means of scaling concepts originally developed for random walks in statistical physics. The series of overnight price differences is mapped onto a one-dimensional random walk: the bond walk. The analysis of the root mean square fluctuation function and of the auto-correlation function indicates the absence of both short- and long-range correlations in the bond walk. A simple Monte Carlo simulation of a random walk with trinomial probability distribution is able to reproduce the main features of the bond walk

    Mixtures of compound Poisson processes as models of tick-by-tick financial data

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    A model for the phenomenological description of tick-by-tick share prices in a stock exchange is introduced. It is based on mixtures of compound Poisson processes. Preliminary results based on Monte Carlo simulation show that this model can reproduce various stylized facts

    On the non-stationarity of financial time series: impact on optimal portfolio selection

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    We investigate the possible drawbacks of employing the standard Pearson estimator to measure correlation coefficients between financial stocks in the presence of non-stationary behavior, and we provide empirical evidence against the well-established common knowledge that using longer price time series provides better, more accurate, correlation estimates. Then, we investigate the possible consequences of instabilities in empirical correlation coefficient measurements on optimal portfolio selection. We rely on previously published works which provide a framework allowing us to take into account possible risk underestimations due to the non-optimality of the portfolio weights being used in order to distinguish such non-optimality effects from risk underestimations genuinely due to non-stationarities. We interpret such results in terms of instabilities in some spectral properties of portfolio correlation matrices

    Activity spectrum from waiting-time distribution

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    In high frequency financial data not only returns but also waiting times between trades are random variables. In this work, we analyze the spectra of the waiting-time processes for tick-by-tick trades. The numerical problem, strictly related with the real inversion of Laplace transforms, is analyzed by using Tikhonov's regularization method. We also analyze these spectra by a rough method using a comb of Dirac's delta functions
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