Market Framework

This chapter describes the analytical framework for financial assets and the system of notation used in this book. It also presents the debate on the measure of the time of markets. We begin by proposing a simple and general formalized convention for assets and portfolios. The notation introduced will be applied throughout this book. In some cases, the traditional notation found in the academic literature or in finance textbooks has been preserved. In other situations, we have used a more intuitive convention. We introduce in a rigorous way connections between empirical professional practices and quantitative finance theories. For example, we link the decomposition of performance to the notion of the stochastic integral. The question of the choice of simple or logarithmic returns is then tackled. We also perform the computation of the corresponding moments…