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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 85, 2013 - Issue 2
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Original Articles

Delay geometric Brownian motion in financial option valuation

Xuerong Mao Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XT, UK
&
Sotirios Sabanis Maxwell Institute for Mathematical Sciences and School of Mathematics, University of Edinburgh, Edinburgh, EH9 3JZ, UKCorrespondence[email protected]
Pages 295-320 | Received 29 Dec 2010, Accepted 21 Dec 2011, Published online: 15 Mar 2012

Citations (23)

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Chaman Kumar & Sotirios Sabanis. (2014) Strong Convergence of Euler Approximations of Stochastic Differential Equations with Delay Under Local Lipschitz Condition. Stochastic Analysis and Applications 32:2, pages 207-228.
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Articles from other publishers (22)

Emmanuel Coffie. (2023) Delay Ait-Sahalia-type interest rate model with jumps and its strong approximation. Statistics & Risk Modeling 40:3-4, pages 67-89.
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Enrico Biffis, Beniamin Goldys, Cecilia Prosdocimi & Margherita Zanella. (2023) A pricing formula for delayed claims: appreciating the past to value the future. Mathematics and Financial Economics 17:2, pages 175-202.
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Lourdes Gómez‐Valle & Julia Martínez‐Rodríguez. (2023) Estimating and pricing commodity futures with time‐delay stochastic processes. Mathematical Methods in the Applied Sciences.
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Sara Biagini, Fausto Gozzi & Margherita Zanella. (2022) Robust Portfolio Choice with Sticky Wages. SIAM Journal on Financial Mathematics 13:3, pages 1004-1039.
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Mahmoud A. Eissa & M. Elsayed. (2022) Improve Stock Price Model-Based Stochastic Pantograph Differential Equation. Symmetry 14:7, pages 1358.
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Vasile Brătian, Ana-Maria Acu, Diana Marieta Mihaiu & Radu-Alexandru Șerban. (2022) Geometric Brownian Motion (GBM) of Stock Indexes and Financial Market Uncertainty in the Context of Non-Crisis and Financial Crisis Scenarios. Mathematics 10:3, pages 309.
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Weijun Meng & Jingtao Shi. (2021) A global maximum principle for stochastic optimal control problems with delay and applications. Systems & Control Letters 150, pages 104909.
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Jing Hai Shao & Kun Zhao. (2020) Continuous Dependence for Stochastic Functional Differential Equations with State-Dependent Regime-Switching on Initial Values. Acta Mathematica Sinica, English Series 37:3, pages 389-407.
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Coffie Emmanuel & Xuerong Mao. (2021) Truncated EM numerical method for generalised Ait-Sahalia-type interest rate model with delay. Journal of Computational and Applied Mathematics 383, pages 113137.
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Nishant Agrawal & Yaozhong Hu. (2020) Jump Models with Delay—Option Pricing and Logarithmic Euler–Maruyama Scheme. Mathematics 8:11, pages 1932.
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Qiang Zhang & Ping Chen. (2019) Optimal Reinsurance and Investment Strategy for an Insurer in a Model with Delay and Jumps. Methodology and Computing in Applied Probability 22:2, pages 777-801.
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Alessandra Cretarola, Gianna Figà-Talamanca & Marco Patacca. (2019) Market attention and Bitcoin price modeling: theory, estimation and option pricing. Decisions in Economics and Finance 43:1, pages 187-228.
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Lisha Lin, Yaqiong Li, Jianhong Wu & Ge Li. (2019) Robustness analysis on the pricing of some options on two assets with delays. Physica A: Statistical Mechanics and its Applications 532, pages 121883.
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Mahmoud A Eissa & Boping Tian. (2018) A stochastic corporate claim value model with variable delay. Journal of Physics: Conference Series 1053, pages 012018.
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Lisha Lin, Yaqiong Li & Jing Wu. (2018) The pricing of European options on two underlying assets with delays. Physica A: Statistical Mechanics and its Applications 495, pages 143-151.
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Chunxiang A & Yi Shao. (2018) Worst-Case Investment Strategy with Delay. Journal of Systems Science and Information 6:1, pages 35-57.
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Jingtao Shi, Juanjuan Xu & Huanshui Zhang. (2015) Stochastic recursive optimal control problem with time delay and applications. Mathematical Control & Related Fields 5:4, pages 859-888.
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Sara Biagini, Fausto Gozzi & Margherita Zanella. (2021) Robust Portfolio Choice With Sticky Wages. SSRN Electronic Journal.
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Enrico Biffis, Gianluca Cappa, Fausto Gozzi & Margherita Zanella. (2021) Optimal Portfolio Choice With Path-Dependent Labor Income: Finite Retirement Time. SSRN Electronic Journal.
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Alessandra Cretarola, Gianna Figg-Talamanca & Marco Patacca. (2017) A Sentiment-Based Model for the Bitcoin: Theory, Estimation and Option Pricing. SSRN Electronic Journal.
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Alessandra Cretarola & Gianna Figg-Talamanca. (2017) A Confidence-Based Model for Asset and Derivative Prices in the Bitcoin Market. SSRN Electronic Journal.
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Enrico Biffis, Ben Goldys & Cecilia Prosdocimi. (2015) A Pricing Formula for Delayed Claims: Appreciating the Past to Value the Future. SSRN Electronic Journal.
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