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Stochastic Modelling on Dynamics of Portfolio Diversifications among the Fixed and Operational Investments through Internal Bivariate Linear Birth, Death and Migration Processes

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Document pages: 16 pages

Abstract: In this paper, a bivariate stochastic process with Poisson postulates has beenconsidered to model the incomings, outgoings and mutual transfers of investmentsbetween and within the portfolios during an epoch of time “t”.Stochastic differential equations were obtained from the simple differentialdifference equations during the epoch of time “Δt”. The notion of bivariatelinear birth, death and migration process has been utilized for measuring variousstatistical characteristics among the investments of Long and Short terms.All possible fluctuations in the investment flow have been considered to exploremore meaningful assumptions with contemporary marketing environments.Mathematical relations for proposed statistical measures such as averagesizes and variances of short term and long-term investments along withthe correlation coefficient between them are derived after obtaining the relateddifferential equations. Numerical illustrations were provided for betterunderstanding of the developed models with practitioner’s point of view.

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