0000000000447641

AUTHOR

Mario Annunziato

showing 2 related works from this author

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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A Fokker–Planck control framework for multidimensional stochastic processes

2013

AbstractAn efficient framework for the optimal control of probability density functions (PDFs) of multidimensional stochastic processes is presented. This framework is based on the Fokker–Planck equation that governs the time evolution of the PDF of stochastic processes and on tracking objectives of terminal configuration of the desired PDF. The corresponding optimization problems are formulated as a sequence of open-loop optimality systems in a receding-horizon control strategy. Many theoretical results concerning the forward and the optimal control problem are provided. In particular, it is shown that under appropriate assumptions the open-loop bilinear control function is unique. The res…

Stochastic controlMathematical optimizationContinuous-time stochastic processOptimization problemoptimal control stochastic processesStochastic processApplied MathematicsOptimal controlComputational MathematicsModel predictive controlMultidimensional stochastic processOptimal control theoryLimit cycleProbability density functionFokker–Planck equationFokker–Planck equationModel predictive controlMathematicsJournal of Computational and Applied Mathematics
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