Mathematical Modelling of an Investor’s Wealth with Different Stochastic Volatility Models
Keywords:
Optimal portfolio distribution, stochastic volatility, Ito’s lemma, Hamilton Jacobi Bellman equation, financial market.Abstract
This paper investigates the application of various stochastic volatility models in determining optimal investment strategies in the stock market. The study explores the geometric Brownian motion (GBM), constant elasticity of variance (CEV), modified CEV (M-CEV), and Heston volatility models. Each model offers a unique perspective on volatility dynamics and option pricing. The research formulates the Hamilton-Jacobi-Bellman (HJB) equations for each model and employs the Legendre transformation method to convert them into linear partial differential equations (PDEs). The quadratic utility function is utilized to derive optimal portfolio distributions under each model. Numerical simulations are conducted to analyze the impact of market parameters such as appreciation rate, volatility, interest rate, elasticity parameter, tax, and investor's wealth on the optimal portfolio distribution. The results indicate that optimal investment strategies vary significantly based on market conditions and investor preferences. Overall, this study provides valuable insights into the dynamic nature of financial markets and offers practical guidance for portfolio optimization and risk management strategies
Most read articles by the same author(s)
- Amadi Ugwulo Chinyere, Modelling Glucose-Insulin Dynamics: Insights for Diabetes Management , Communication In Physical Sciences: Vol. 11 No. 3 (2024): VOLUME 11 ISSUE 3
- Amadi Ugwulo Chinyere, Modelling Glucose-Insulin Dynamics: Insights for Diabetes Management , Communication In Physical Sciences: Vol. 11 No. 3 (2024): VOLUME 11 ISSUE 3
Similar Articles
- Yusuf Mohammad Auwal, Hussaini Shuaibu, Muhammad Sani Isa, Study of Symmetric Nuclear Matter Properties in Non-linear Walecka Model via Relativistic Mean-field approximation at zero-temperature , Communication In Physical Sciences: Vol. 12 No. 2 (2025): VOLUME 12 ISSUE 2
- Akaezue Nelson Nwagbogwu, Ngiangia Alalibor Thompson, Onyeaju Michael Chukwudi, Thermal Properties of Diffusing Species into Some Host Metals , Communication In Physical Sciences: Vol. 11 No. 4 (2024): VOLUME 11 ISSUE 4
- Benjamin Effiong, Emmanuel Akpan, Specification Procedure For Symmetric Smooth Transition Autoregressive Models , Communication In Physical Sciences: Vol. 12 No. 2 (2025): VOLUME 12 ISSUE 2
- Esharive Ogaga, Onimisi Martins, Abdulateef Onimisi Jimoh, Akudo Ernest orji, Aigbadon Godwin Okumagbe, Achegbulu Ojonimi Emmanuel, Assessment of Geotechnical Attributes of Laterites as Sub-base and Sub-Grade Materials in Parts of Northern Anambra Basin Nigeria: Implications for Road Pavement Construction. , Communication In Physical Sciences: Vol. 11 No. 3 (2024): VOLUME 11 ISSUE 3
- Esharive Ogaga, Onimisi Martins, Abdulateef Onimisi Jimoh, Akudo Ernest orji, Aigbadon Godwin Okumagbe, Achegbulu Ojonimi Emmanuel, Assessment of Geotechnical Attributes of Laterites as Sub-base and Sub-Grade Materials in Parts of Northern Anambra Basin Nigeria: Implications for Road Pavement Construction , Communication In Physical Sciences: Vol. 11 No. 3 (2024): VOLUME 11 ISSUE 3
- Osaghae Edgar O, Obi Jonathan Chukwuyeni, Solving towers of Hanoi problem using 2-Consecutive moves Algorithm , Communication In Physical Sciences: Vol. 10 No. 3 (2023): VOLUME 10 ISSUE 3
- Eno John, Promise Asukwo, Nkem Ogbonna, Convergence Analysis of Sinc-Collocation Scheme With Composite Trigonometric Function for Fredholm Integral Equations of the Second Kind , Communication In Physical Sciences: Vol. 11 No. 3 (2024): VOLUME 11 ISSUE 3
- Oladimeji Enock Oluwole, Umeh Emmanuel Chukwuebuka, Idundun Victory Toritseju, Koffa Durojaiye Jude, Obaje Vivian Onechojo , Adeleke Joshua Toyin, Petinrin Moses Omolayo , The performance analysis of a Wood-Saxon driven Quantum-Mechanical Carnot Engine , Communication In Physical Sciences: Vol. 11 No. 3 (2024): VOLUME 11 ISSUE 3
- Christabel M. Eteghwia, Enoo Ojaikre, Efeturi A. Onoabedje, Chinweike C. Eze, Patience O. Adomi, 7-Chloroquinoline Sulphonamide Derivatives: Synthesis, Characterization, Biological and Drug-likeness Evaluation , Communication In Physical Sciences: Vol. 12 No. 1 (2024): VOLUME 12 ISSUE 1
- Aniekan Udongwo, Oluwafisayomi Folorunso, Resource Recovery from Maize Biomass for the Synthesis of SiO2 Nanoparticles and Crystallographic Analysis for Possible Applications , Communication In Physical Sciences: Vol. 12 No. 2 (2025): VOLUME 12 ISSUE 2
You may also start an advanced similarity search for this article.