Mathematics of the Bond Market: A Lévy Processes Approach (Encyclopedia of Mathematics and its Applications)

Mathematical models of bond markets are of interest to researchers working in applied mathematics, especially in mathematical finance. This book concerns bond market models in which random elements are represented by Lévy processes. These are more flexible than classical models and are well suited to describing prices quoted in a discontinuous fashion. The book's key aims are to characterize bond markets that are free of arbitrage and to analyze their completeness. Nonlinear stochastic partial differential equations (SPDEs) are an important tool in the analysis. The authors begin with a relatively elementary analysis in discrete time, suitable for readers who are not familiar with finance or continuous time stochastic analysis. The book should be of interest to mathematicians, in particular to probabilists, who wish to learn the theory of the bond market and to be exposed to attractive open mathematical problems. "Bonds are financial assets issued by governments, central banks or companies. Their holders receive some fixed payments at future dates. The life time of a bond is specified by its maturity - the date when the nominal value of the bond is paid. All previous payments are called coupons and they are usually fixed as fractions of the nominal value of the bond. The payments received by the holder, although fixed, can, however, be influenced by the credit rating of the issuer. This means that in case of the issuer's bankruptcy the promised payments can be reduced or even canceled"-- Provided by publisher Analyses Bond Market Models With Lévy Stochastic Factors, Suitable For Graduates And Researchers In Probability And Mathematical Finance.