Amir Sadr - Mathematical Techniques in Finance

Corporations raise capital by issuing stock (equity), which is publicly traded. Households participate in the stock market directly via brokerage accounts or retirement plans primarily investing in mutual funds and ETFs (Exchange Traded Funds). The allocation of investments between different assets or funds is the subject of portfolio selection.

Firms and households use insurance and derivatives markets to mitigate and manage financial risk. Consumers buy home and auto insurance to protect against loss. Corporations raise money from the capital markets and manage their interest rate exposure through interest rate swaps and derivatives. Producers use commodity futures and derivatives to manage price risk, and pension plans and investors use equity derivatives for risk management and speculation.

Households, corporations, governments, and financial firms, such as commercial and investment banks, insurance companies, asset management companies, and hedge funds, all participate in financial markets and employ a variety of products and increasingly sophisticated quantitative methods (see Table 1.6). The mathematics includes results and techniques from calculus, linear algebra, probability and statistics, numerical methods, optimization techniques, stochastic processes, differential equations, and machine learning techniques. In the following chapters, we will introduce these techniques as used in different markets and financial products.

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