Random Evolutions and their Applications: New Trends / Edition 1

by Anatoly Swishchuk

Overview

The book is devoted to the new trends in random evolutions and their various applications to shastic evolutionary sytems (SES). Such new developments as the analogue of Dynkin's formulae, boundary value problems, shastic stability and optimal control of random evolutions, shastic evolutionary equations driven by martingale measures are considered. The book also contains such new trends in applied probability as shastic models of financial and insurance mathematics in an incomplete market. In the famous classical financial mathematics Black-Scholes model of a (B,S)­ market for securities prices, which is used for the description of the evolution of bonds and sks prices and also for their derivatives, such as options, futures, forward contracts, etc., it is supposed that the dynamic of bonds and sks prices are set by a linear differential and linear shastic differential equations, respectively, with interest rate, appreciation rate and volatility such that they are predictable processes. Also, in the Arrow-Debreu economy, the securities prices which support a Radner dynamic equilibrium are a combination of an Ito process and a random point process, with the all coefficients and jumps being predictable processes.

Product Details

ISBN-13:	9789048154418
Publisher:	Springer Netherlands
Publication date:	12/07/2010
Series:	Mathematics and Its Applications , #504
Edition description:	Softcover reprint of hardcover 1st ed. 2000
Pages:	294
Product dimensions:	6.30(w) x 9.45(h) x 0.03(d)

Table of Contents

1 Random Evolutions (RE).- 2 Shastic Evolutionary Systems.- 3 Random Evolution Equations Driven by Space-Time White Noise.- 4 Analogue of Dynkin’s Formula (ADF) for Multiplicative Operator Functionals (MOF), RE and SES.- 5 Boundary Value Problems (BVP) for RE and SES.- 6 Shastic Stability of RE and SES.- 7 Shastic Optimal Control of Random Evolutions and SES.- 8 Statistics of SES.- 9 Random Evolutions in Financial Mathematics Incomplete Market.- 10 Random Evolutions in Insurance Mathematics. Incomplete Market.- 11 Shastic Stability of Financial and Insurance Shastic Models.- 12 Shastic Optimal Control of Financial and Insurance Shastic Models.- 13 Statistics of Financial Shastic Models.