Private Math, Physics, Statistics Tutoring on ALL LEVELS! Promise to show ?beyond the cookbook? solutions for any problem --- real understanding is the key! While ?cookbook methods? will work on some sample problems, they will not work on real tests! My real specialty is Advanced Statistics, but I also specialize in pretty much all other areas in Math, Physics and Statistics: Algebra, Calculus, Geometry as well as more advanced areas (like Linear Algebra, Multivariate Calculus, etc.). In... [more]
Understanding Differential Equations is an integral part of the my Financial Math degree. In fact, Black Scholes equation is really a partial differential equations which is "one step higher" as compared to the Ordinary Differential Equations. In addition, I've taken classes have expertise in the following types of ODE's: --- ODE's with "separable variables" --- first-order linear ODE's --- linear homogeneous and non-homogeneous ODE's --- systems of linear first order ODE's
I am an experienced actuarial science instruction with a master's degree in Financial Math and certification from SOA. Probability distributions, conditional probabilities, expectations, moment generating functions; we cover it all...
Linear Algebra is a big part of Risk Management and Portfolio Construction in Financial Math. In addition to my MS in FinMath from University of Chicago, I've also passed the final exam in Advanced Risk and Portfolio Management Bootcamp. Estimating covariance matrix and diagonalizing it via eigenvectors and their eigenvalues is an exercise which I've done many times in the past. Another area which comes up many times in Financial Math and inseparably related to Linear Algebra is Regression Analysis, i.e. x_hat = (A_t*A)^(-1) * (A_t*b). Yet another area of my expertise (and also connected to Financial Math) is the notion of positive definite matrix (like covariance matrix) or positive semi-definite matrix. This is closely related to calculating the variance of the portfolio via Var = x_t*sigma*x (the idea that covariance matrix is positive definite is the same as stating that portfolio could not possibly have negative variance, no matter what the weights of the constituent securities are). This is also related to the idea of symmetric matrices and why their eigenvalues have to be real (easily shown with linear algebra equations).
I've been using Matlab for over eight years since I started my master's degree in financial math at University of Chicago. Since then, I've done numerous projects in Matlab both academically and professionally while working as a Desk Quant at Hedge Funds. In many ways, properly using and understanding Matlab parallels my knowledge of linear algebra. Once one understands how to set up a problem using vectors and matrices, Matlab makes it easy to "take it from there".