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In 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.
In 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.
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