(a) Given a correlation matrix A, 1.0 0.5 0.2 A 0.5 1.0 -0.4 0.2 -0.4 1.0 perform a Cholesky decomposition of the matrix A, which is a decomposition of the form A = LLT, when A is symmetric and positive definite matrix. The function you construct should return the lower triangular matrix, L. Consider three assets, starting with S(0) = [100, 101,98). The assets are assumed to follow a standard geometric Brownian motion of the form dS:(t) = MiS:(t)dt + 0,S:(t)dW.(t). We assume u = [0.03, 0.06, 0.02), the volatility o = [0.05, 0.2, 0.15), and the BM's have the correlation matrix A (e.g., d = 212dt = 0.5dt). (a) Given a correlation matrix A, 1.0 0.5 0.2 A 0.5 1.0 -0.4 0.2 -0.4 1.0 perform a Cholesky decomposition of the matrix A, which is a decomposition of the form A = LLT, when A is symmetric and positive definite matrix. The function you construct should return the lower triangular matrix, L. Consider three assets, starting with S(0) = [100, 101,98). The assets are assumed to follow a standard geometric Brownian motion of the form dS:(t) = MiS:(t)dt + 0,S:(t)dW.(t). We assume u = [0.03, 0.06, 0.02), the volatility o = [0.05, 0.2, 0.15), and the BM's have the correlation matrix A (e.g., d = 212dt = 0.5dt)