Mathematical modelling of financial risks. Theory of measurement (Q2776777)

The goal of this small book is to provide a strict stochastic background to the various notions of risk and risk measurement, which are widely used in mathematical finance, actuarial sciences and other fields of applied mathematics.NEWLINENEWLINEThe main part of the book is devoted to one-period analysis. We model the gain (return) from a risky investment by a random variable. Hence, the risk measure is a mapping from a certain set of random variables to \(\mathbb R\). The author describes the several measures of risk, which are used in practice or in the theory, and investigates their properties, especially the compatibility with various stochastic preorderings (dominances) and convexity.NEWLINENEWLINE In the last chapter, basing on the so called ruin process, the author introduces the reader to a multiperiod problem of risk management.