The exhaustive list of topics in Mathematical Finance in which we provide Help with Homework Assignment and Help with Project is as follows:

- Basics of Financial Markets: Main theme of mathematical finance, financial markets and terminology, time value of money, interest rate, discount rate, bonds and bonds pricing, yield curves, duration and convexity, term structure of interest rates, spot and forward rates, net present value, net future value, financial instruments, underlying and derivative securities, types of derivatives, options, forwards, futures, swaps, concept of arbitrage.
- Portfolio Modeling and Analysis: Portfolios, returns and risk, risk-reward analysis, asset pricing models, mean variance portfolio optimization, Markowitz model and efficient frontier calculation algorithm, Capital Asset Pricing Models (CAPM).
- Probability Essentials: Probability spaces, filtrations as information content, random variables, conditional expectations, Definition and classification of random processes, martingales.
- Discrete-time Finance: Pricing by arbitrage, risk-neutral probability measures, valuation of contingent claims, fundamental theorem of asset pricing, Cox-Ross-Rubinstein (CRR) model, pricing and hedging of European and American derivatives as well as fixed-income derivatives in CRR model, general results related to prices of derivatives.
- Stochastic Calculus: Brownian motion, martingales, Itô’s formula, Itô integral, risk-neutral measure, SDE; Risk-neutral measure, Girsanov's theorem for change of measure, martingale representation theorems, representation of Brownian martingales, Feynman-Kac formula.
- Continuous-time Finance: Black-Scholes-Merton model of stock prices as geometric Brownian motion, derivation of the Black-Scholes-Merton partial differential equation, the Black-Scholes formula and simple extensions of the model, self-financing strategies and model completeness, risk neutral measures, the fundamental theorems of asset pricing, continuous time optimal stopping and pricing of American options, forwards and futures in Black-Scholes-Merton model.