On Chaos Representation and Orthogonal Polynomials for the Doubly Stochastic Poisson Process

Nunno, Giulia Di; Sjursen, Steffen

doi:10.1007/978-3-0348-0545-2_2

Cited by 7 publications

(4 citation statements)

References 20 publications

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“…Specifically, the following explicit stochastic representation theorem is considered in the sequel. See the original version in [20] and the versions for random fields appearing in [22,28].…”

Section: Definitionmentioning

confidence: 99%

On stochastic control for time changed Lévy dynamics

Nunno

2022

SeMA

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Controlled stochastic differential equations driven by time changed Lévy noises do not enjoy the Markov property in general, but can be treated in the framework of general martingales. From the modelling point of view, time changed noises constitute a feasible way to include time dependencies at noise level and still keep a reasonably simple structure. Furthermore, they are easy to simulate, with the result that time change Lévy dynamics attract attention in various fields of application. In this work we survey an approach to stochastic control via maximum principle for time changed Lévy dynamics. We emphasise the role and use of different information flows in tackling the various control problems. We show how these techniques can be extended to include Volterra type dynamics and the control of forward–backward systems of equations. Our techniques make use of the stochastic non-anticipating (NA) derivative in a general martingale framework.

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Section: Definitionmentioning

confidence: 99%

On stochastic control for time changed Lévy dynamics

Nunno

2022

SeMA

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“…Before entering the core of the issue we present the necessary results related to mean-field BSDEs. We follow the approach of [4] and exploit the techniques suggested in [9] and [10] for time changed Lévy noises.…”

Section: Mean-field Bsdesmentioning

confidence: 99%

“…It is well known that we can obtain these results for mixtures of Gaussian and Poisson type measures and in [9] it is proved for time changed Brownian and time changed Poisson random measures. See also [10] for a specific study on the structure of the doubly stochastic Poisson random noises.…”

Section: Introductionmentioning

confidence: 99%

A Maximum Principle for Mean-Field SDEs with Time Change

Nunno

Haferkorn

2017

Appl Math Optim

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Time change is a powerful technique for generating noises and providing flexible models. In the framework of time changed Brownian and Poisson random measures we study the existence and uniqueness of a solution to a general mean-field stochastic differential equation. We consider a mean-field stochastic control problem for mean-field controlled dynamics and we present a necessary and a sufficient maximum principle. For this we study existence and uniqueness of solutions to mean-field backward stochastic differential equations in the context of time change. An example of a centralised control in an economy with specialised sectors is provided.

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“…More generally, integration by parts formulas for discrete and jump processes can be obtained using multiple stochastic integral expansions and finite difference operators, or the absolute continuity of jump times. Since [1,5] have established chaotic representations for continuous-time Markov chains and point processes, respectively, multiple stochastic integral expansions for random functionals were built in, for example, [9,17,20].…”

Section: Introductionmentioning

confidence: 99%

An Improvement of Markovian Integration by Parts Formula and Application to Sensitivity Computation

Liu

Shi²,

Tang³

et al. 2021

Prob. Eng. Inf. Sci.

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This paper establishes a new version of integration by parts formula of Markov chains for sensitivity computation, under much lower restrictions than the existing researches. Our approach is more fundamental and applicable without using Girsanov theorem or Malliavin calculus as did by past papers. Numerically, we apply this formula to compute sensitivity regarding the transition rate matrix and compare with a recent research by an IPA (infinitesimal perturbation analysis) method and other approaches.

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On Chaos Representation and Orthogonal Polynomials for the Doubly Stochastic Poisson Process

Cited by 7 publications

References 20 publications

On stochastic control for time changed Lévy dynamics

On stochastic control for time changed Lévy dynamics

A Maximum Principle for Mean-Field SDEs with Time Change

An Improvement of Markovian Integration by Parts Formula and Application to Sensitivity Computation

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