Speaker: Cristian Amador Loli Prudencio, San Marcos e UFF.
Date: 04 nov 2022, 11h.
Place: Room 407, Bloco H, Campus Gragoatá, UFF.
Abstract: In the present work we analyze the Model of a Stochastic Differential Equation of Black-Scholes associated with a Financial behavior, which we transform by stochastic methods into a PDE, we do the analysis, the discretization and we finish with the computational simulation using Matlab.
The Black-Scholes model is given in stochastic form by the equation
dS(t)=μS(t)dt+σS(t)dW(t), 0≤t≤T
S(0)=S0
which, by stochastic and deterministic processes, we lead to a retrograde parabolic partial differential equation, we study the equation, we discretize it by Finite Differences, we analyze the convergence and stability, and finally we do the implementation and computational simulation.
Keywords: Black-Scholes, Brownian Motion, Itô, Finite Differences, Convergence.