Model of Stabilizing of the Interest Rate on Deposits Banking System Using by Moment Equations

Dzhalladova, Irada; Michalková, Mária; Růžičková, Miroslava

doi:10.2478/tmmp-2013-0004

Cited by 5 publications

(6 citation statements)

References 20 publications

(10 reference statements)

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“…If system (1) has no jumps, then the moment Equations (23) and (24) coincide with those obtained in [6].…”

Section: Remarksupporting

confidence: 71%

“…Many real processes in both research and practice can be well modelled by dynamical systems with random parameters. Dynamical systems of this kind are widely used for modelling in biology and medicine [1], in sociology or socioeconomics [2,3], and in finance [4][5][6][7][8]. They can also be applied to modelling security and risk management in cyberspace [9,10] and in many other areas.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Dynamical System with Random Parameters as a Mathematical Model of Real Phenomena

Diblı́k

Dzhalladova²,

Růžičková

2019

Symmetry

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In many cases, it is difficult to find a solution to a system of difference equations with random structure in a closed form. Thus, a random process, which is the solution to such a system, can be described in another way, for example, by its moments. In this paper, we consider systems of linear difference equations whose coefficients depend on a random Markov or semi-Markov chain with jumps. The moment equations are derived for such a system when the random structure is determined by a Markov chain with jumps. As an example, three processes: Threats to security in cyberspace, radiocarbon dating, and stability of the foreign currency exchange market are modelled by systems of difference equations with random parameters that depend on a semi-Markov or Markov process. The moment equations are used to obtain the conditions under which the processes are stable.

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“…If system (1) has no jumps, then the moment Equations (23) and (24) coincide with those obtained in [6].…”

Section: Remarksupporting

confidence: 71%

Section: Introductionmentioning

confidence: 99%

A Dynamical System with Random Parameters as a Mathematical Model of Real Phenomena

Diblı́k

Dzhalladova²,

Růžičková

2019

Symmetry

Self Cite

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“…It is very natural to involve randomness into physical systems while solving problems in economics and finance, see for example [5]. In last 50 years, systems with random effects are considered in many fields as biology, chemistry, physics and engineering.…”

Section: Resultsmentioning

confidence: 99%

Stochastic Differential Equations Describing Systems with Coloured Noise

Kolarova

Brančík

2018

Tatra Mountains Mathematical Publications

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In this paper we deal with stochastic differential equations, that describe systems effected by coloured noise. In electrical systems this can be the case, when e.g. transmission line is modelled by means of proper higher-order ladder network. We define the mathematical representation of the coloured noise as a solution of the Langevin equation and formulate the corresponding Itô type stochastic differential equation. Applying this theory we derive the stochastic model of the network and find sets of individual stochastic trajectories numerically via a stochastic version of the backward Euler scheme. Afterwards respective confi-dence intervals are computed statistically while utilizing Student’s t distribution. The theoretical results are illustrated by an example of a higher-order ladder network. Numerical simulations in the example are carried out using Matlab.

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“…Theorem 2.1. [3] Let (Ω, F, P ) be a probability space where Ω is a sample space, F is set of all events (the σ-algebra) and P is some probability measure. Let…”

Section: Expected Value Of Principalmentioning

confidence: 99%

Mathematical model of marketing strategy in banking

Michalková¹,

Michalkova²

2016

ams

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Based on the marketing strategy of product modification we discuss the time deposit with randomly changing interest. The change of the interest rate depends on whether the client is treated to a special interest rate or not. As it is shown in the paper the coefficients of the equation are changing in accordance with a homogeneous Markov chain. Therefore we use moment equations to model the expected value of principal every month. The growth of the principal is expressed by a stochastic difference equation that is transformed to a system of moment equations of first order. These equations are ordinary difference equations that can be solved using known methods.

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Model of Stabilizing of the Interest Rate on Deposits Banking System Using by Moment Equations

Cited by 5 publications

References 20 publications

A Dynamical System with Random Parameters as a Mathematical Model of Real Phenomena

A Dynamical System with Random Parameters as a Mathematical Model of Real Phenomena

Stochastic Differential Equations Describing Systems with Coloured Noise

Mathematical model of marketing strategy in banking

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