Search results for "IMEX numerical method"

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CALIBRATION OF LÉVY PROCESSES USING OPTIMAL CONTROL OF KOLMOGOROV EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS

2018

We present an optimal control approach to the problem of model calibration for L\'evy processes based on a non parametric estimation procedure. The calibration problem is of considerable interest in mathematical finance and beyond. Calibration of L\'evy processes is particularly challenging as the jump distribution is given by an arbitrary L\'evy measure, which form a infinite dimensional space. In this work, we follow an approach which is related to the maximum likelihood theory of sieves. The sampling of the L\'evy process is modelled as independent observations of the stochastic process at some terminal time $T$. We use a generic spline discretization of the L\'evy jump measure and selec…

non-parametric maximum likelihood methodOptimization problemDiscretizationL ́evy processesoptimal control of PIDE010103 numerical & computational mathematics01 natural sciences93E10 (primary) 49K20 60G51 62G05 (secondary)010104 statistics & probabilitysymbols.namesakeConjugate gradient methodIMEX numerical methodQA1-939Applied mathematics0101 mathematicsMathematics - Optimization and ControlMathematicsKolmogorov-Fokker-Planck equationoptimal control of PIDE Kolmogorov-Fokker-Planck equation L ́evy processes non-parametric maximum likelihood method IMEX numerical method.SolverOptimal controlSpline (mathematics)Lévy processesModeling and SimulationLagrange multipliersymbolsAkaike information criterionMathematicsAnalysisMathematical Modelling and Analysis
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