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1

  • Numerical Analysis on Growth of Angiogenesis Cancer with delay differential equations



Mr. John Abhishek Masih1, Prof. Rajiv Phillip2, Manish Sharma3

Abstract:
A mathematical model presented with the help of delay differential equations and a systematic study of the growth on angiogenesis cancer. This model is investigated using stability theory as well as equilibria. Using the theory of delay differential equations and the basic reproduction R_0 is a measure of the potential for disease spread in a population. We observe that the growth of cancer infection free equilibrium is unstable because the basic reproduction number R_0<1.


11-19
2

  • Comparison of Stochastic Volatility Jump Diffusion Model without Shot Noise With Heston Model



Jitendra Singh

Abstract:
One well-known issue with the standard Black-Scholes (BS) approach when attempting to simulate option pricing or asset returns is that it is impossible to duplicate the observed skews/smiles for the second case and the empirical features of asset returns for the first. Adding jumps or stochastic volatility to the underlying process is a popular solution to this issue. This paper studies the stochastic volatility jump diffusion(SVJD) model without shot noise(SN) and compare with Heston model. Further, it is reviewing their theoretical properties, and focusing on their ability to model asset returns by analyzing their statistical properties. The models are calibrated usingU.S. OIL FUND (ETF) (NYSEArca: USO) option prices. Finally, numerical illustration of SVJD models without SN are consistent with the real data in compare to Heston model.


20-28
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