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Books > Science & Mathematics > Mathematics > Applied mathematics
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Inhomogeneous Random Evolutions and Their Applications (Hardcover)
Loot Price: R4,731
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Inhomogeneous Random Evolutions and Their Applications (Hardcover)
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Inhomogeneous Random Evolutions and Their Applications explains how
to model various dynamical systems in finance and insurance with
non-homogeneous in time characteristics. It includes modeling for:
financial underlying and derivatives via Levy processes with
time-dependent characteristics; limit order books in the
algorithmic and HFT with counting price changes processes having
time-dependent intensities; risk processes which count number of
claims with time-dependent conditional intensities; multi-asset
price impact from distressed selling; regime-switching Levy-driven
diffusion-based price dynamics. Initial models for those systems
are very complicated, which is why the author's approach helps to
simplified their study. The book uses a very general approach for
modeling of those systems via abstract inhomogeneous random
evolutions in Banach spaces. To simplify their investigation, it
applies the first averaging principle (long-run stability property
or law of large numbers [LLN]) to get deterministic function on the
long run. To eliminate the rate of convergence in the LLN, it uses
secondly the functional central limit theorem (FCLT) such that the
associated cumulative process, centered around that deterministic
function and suitably scaled in time, may be approximated by an
orthogonal martingale measure, in general; and by standard Brownian
motion, in particular, if the scale parameter increases. Thus, this
approach allows the author to easily link, for example, microscopic
activities with macroscopic ones in HFT, connecting the parameters
driving the HFT with the daily volatilities. This method also helps
to easily calculate ruin and ultimate ruin probabilities for the
risk process. All results in the book are new and original, and can
be easily implemented in practice.
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