TITLE:
Stochastic Modelling on Dynamics of Portfolio Diversifications among the Fixed and Operational Investments through Internal Bivariate Linear Birth, Death and Migration Processes
AUTHORS:
Tirupathi Rao Padi, Chiranjeevi Gudala
KEYWORDS:
Stochastic Modelling, Portfolio Diversification, Difference-Differential Equations
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.8,
August
31,
2017
ABSTRACT: In this paper, a bivariate stochastic process with Poisson postulates has been
considered to model the incomings, outgoings and mutual transfers of investments
between and within the portfolios during an epoch of time “t”.
Stochastic differential equations were obtained from the simple differential
difference equations during the epoch of time “Δt”. The notion of bivariate
linear birth, death and migration process has been utilized for measuring various
statistical characteristics among the investments of Long and Short terms.
All possible fluctuations in the investment flow have been considered to explore
more meaningful assumptions with contemporary marketing environments.
Mathematical relations for proposed statistical measures such as average
sizes and variances of short term and long-term investments along with
the correlation coefficient between them are derived after obtaining the related
differential equations. Numerical illustrations were provided for better
understanding of the developed models with practitioner’s point of view.