Abstract
Abstract In this study, a new method to obtain approximate probability density function (pdf) of random variable of solution of stochastic differential equations (SDEs) by using generalized entropy optimization methods (GEOM) is developed. By starting given statistical data and Euler–Maruyama (EM) method approximating SDE are constructed several trajectories of SDEs. The constructed trajectories allow to obtain random variable according to the fixed time. An application of the newly developed method includes SDE model fitting on weekly closing prices of Honda Motor Company stock data between 02 July 2018 and 25 March 2019.
Highlights
Stochastic differential equation (SDE) is a differential equation in which one or more of the terms are a stochastic process, resulting in a solution which is itself a stochastic process
The results show that (MinMaxEnt)m and (MaxMaxEnt)m distributions obtained by generalized entropy optimization methods (GEOM) is suitable for the assessment of Honda Motor Company (HMC) stock data
It is obtained that HMC stock data and approximate EM values of X, i = 16, 39 are fit to selected SDE model
Summary
Stochastic differential equation (SDE) is a differential equation in which one or more of the terms are a stochastic process, resulting in a solution which is itself a stochastic process. Even if exact solution is known everywhere, this solution may not be available in the computational sense For this reason numeric solution of SDEs acquires an important significance. For 0 ≤ t ≤ T where X(0, ·)εHRV , X(t, ω) is a stochastic process but not a deterministic function.W (t, ω) = W (t) is a Wiener process or Brownian motion which satisfies the following three conditions: 1. It is assumed that the functions f and g are non-anticipating and satisfy the following conditions (c1) and (c2) for some constant k ≥ 0 of existence and uniqueness theorem of solution of SDE model [10]. There are many methods for determining the solution of SDE model (2).
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