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.
1100014993
Random Evolutions and their Applications: New Trends
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.
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Random Evolutions and their Applications: New Trends
294
Random Evolutions and their Applications: New Trends
294Paperback(Softcover reprint of hardcover 1st ed. 2000)
$109.99
109.99
In Stock
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) |
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