Approximation of optimal prices when basic data are weakly dependent

Tatsuhiko Saigo; Hiroshi Takahashi; Ken Ichi Yoshihara

Approximation of optimal prices when basic data are weakly dependent

Tatsuhiko Saigo, Hiroshi Takahashi, Ken Ichi Yoshihara

Research output: Contribution to journal › Article › peer-review

Abstract

Corresponding to the Black-Scholes stochastic differential equation, Yoshihara (2012) introduced a difference equation based on weakly dependent stationary random variables and proved that its solution converges almost surely to a geometric Brownian motion with an annual drift parameter and a volatility which come from the assumption on the random variables. In this paper, we show some further results and present their applications by using approximations of some optimal prices in the Black-Scholes market.

Original language	English
Pages (from-to)	217-230
Number of pages	14
Journal	Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
Volume	23
Issue number	3
Publication status	Published - 2016
Externally published	Yes

Keywords

Black-Scholes type stochastic differential equation
Difference equation
Stationary sequence
Weakly dependent random variable
Wiener process

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Cite this

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title = "Approximation of optimal prices when basic data are weakly dependent",

abstract = "Corresponding to the Black-Scholes stochastic differential equation, Yoshihara (2012) introduced a difference equation based on weakly dependent stationary random variables and proved that its solution converges almost surely to a geometric Brownian motion with an annual drift parameter and a volatility which come from the assumption on the random variables. In this paper, we show some further results and present their applications by using approximations of some optimal prices in the Black-Scholes market.",

keywords = "Black-Scholes type stochastic differential equation, Difference equation, Stationary sequence, Weakly dependent random variable, Wiener process",

author = "Tatsuhiko Saigo and Hiroshi Takahashi and Yoshihara, {Ken Ichi}",

note = "Funding Information: The authors thank Professor S. Sathananthan for giving an opportunity to talk in the Stochastic Algorithms, Analysis and Applications session in the 9th International Conference on Differential Equations and Dynamical Systems. Part of this research was done during the visit by the second author to Texas AandM University, Dallas, whose kind hospitality is gratefully acknowledged. The research is supported by JSPS KAKENHI Grant number 26800063. Publisher Copyright: Copyright {\textcopyright}2016 Watam Press.",

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language = "English",

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AU - Saigo, Tatsuhiko

AU - Takahashi, Hiroshi

AU - Yoshihara, Ken Ichi

N1 - Funding Information: The authors thank Professor S. Sathananthan for giving an opportunity to talk in the Stochastic Algorithms, Analysis and Applications session in the 9th International Conference on Differential Equations and Dynamical Systems. Part of this research was done during the visit by the second author to Texas AandM University, Dallas, whose kind hospitality is gratefully acknowledged. The research is supported by JSPS KAKENHI Grant number 26800063. Publisher Copyright: Copyright ©2016 Watam Press.

PY - 2016

Y1 - 2016

N2 - Corresponding to the Black-Scholes stochastic differential equation, Yoshihara (2012) introduced a difference equation based on weakly dependent stationary random variables and proved that its solution converges almost surely to a geometric Brownian motion with an annual drift parameter and a volatility which come from the assumption on the random variables. In this paper, we show some further results and present their applications by using approximations of some optimal prices in the Black-Scholes market.

AB - Corresponding to the Black-Scholes stochastic differential equation, Yoshihara (2012) introduced a difference equation based on weakly dependent stationary random variables and proved that its solution converges almost surely to a geometric Brownian motion with an annual drift parameter and a volatility which come from the assumption on the random variables. In this paper, we show some further results and present their applications by using approximations of some optimal prices in the Black-Scholes market.

KW - Black-Scholes type stochastic differential equation

KW - Difference equation

KW - Stationary sequence

KW - Weakly dependent random variable

KW - Wiener process

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JF - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

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Approximation of optimal prices when basic data are weakly dependent

Abstract

Keywords

ASJC Scopus subject areas

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