000 04273nam a22005175i 4500
001 978-3-642-13694-8
003 DE-He213
005 20140220084539.0
007 cr nn 008mamaa
008 100721s2010 gw | s |||| 0|eng d
020 _a9783642136948
_9978-3-642-13694-8
024 7 _a10.1007/978-3-642-13694-8
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aPlaten, Eckhard.
_eauthor.
245 1 0 _aNumerical Solution of Stochastic Differential Equations with Jumps in Finance
_h[electronic resource] /
_cby Eckhard Platen, Nicola Bruti-Liberati.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _aXXVI, 856p. 169 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aStochastic Modelling and Applied Probability,
_x0172-4568 ;
_v64
505 0 _aStochastic Differential Equations with Jumps -- Exact Simulation of Solutions of SDEs -- Benchmark Approach to Finance and Insurance -- Stochastic Expansions -- to Scenario Simulation -- Regular Strong Taylor Approximations with Jumps -- Regular Strong Itô Approximations -- Jump-Adapted Strong Approximations -- Estimating Discretely Observed Diffusions -- Filtering -- Monte Carlo Simulation of SDEs -- Regular Weak Taylor Approximations -- Jump-Adapted Weak Approximations -- Numerical Stability -- Martingale Representations and Hedge Ratios -- Variance Reduction Techniques -- Trees and Markov Chain Approximations -- Solutions for Exercises.
520 _aIn financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.
650 0 _aMathematics.
650 0 _aFinance.
650 0 _aDistribution (Probability theory).
650 0 _aEconomics
_xStatistics.
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aStatistics for Business/Economics/Mathematical Finance/Insurance.
650 2 4 _aQuantitative Finance.
700 1 _aBruti-Liberati, Nicola.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642120572
830 0 _aStochastic Modelling and Applied Probability,
_x0172-4568 ;
_v64
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-13694-8
912 _aZDB-2-SMA
999 _c112322
_d112322