Stochastic Analysis for Finance with Simulations (Universitext)
Presents the mathematical methods required for pricingfinancial derivativesEncourages hands-on experience and builds intuition byexplaining theoretical concepts with computer simulationsCovers mathematical prerequisites, including measure theory,ordinary differential equations, and partial differentialequations——————————This book is an introduction to stochastic analysis andquantitative finance; it includes both theoretical andcomputational methods. Topics covered are stochastic calculus,option pricing, optimal portfolio investment, and interest ratemodels. Also included are simulations of stochastic phenomena,numerical solutions of the Black–Scholes–Merton equation, MonteCarlo methods, and time series. Basic measure theory is used as atool to describe probabilistic phenomena.The level of familiarity with computer programming is kept to aminimum. To make the book accessible to a wider audience, somebackground mathematical facts are included in the first part of thebook and also in the appendices. This work attempts to bridge thegap between mathematics and finance by using diagrams, graphs andsimulations in addition to rigorous theoretical exposition.Simulations are not only used as the computational method inquantitative finance, but they can also facilitate an intuitive anddeeper understanding of theoretical concepts.Stochastic Analysis for Finance with Simulations isdesigned for readers who want to have a deeper understanding of thedelicate theory of quantitative finance by doing computersimulations in addition to theoretical study. It will particularlyappeal to advanced undergraduate and graduate students inmathematics and business, but not excluding practitioners infinance industry.