On the class of distributions of subordinated Lévy processes and bases

Sauri, Orimar; Veraart, Almut E. D.

doi:10.1016/j.spa.2016.06.015

Cited by 4 publications

(2 citation statements)

References 27 publications

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“…For a survey on the subject we can refer to [38]. On the other side, the problem of determining the time change given the observations of X and fixed the base process (as a Brownian motion W , or even a Lévy process L) is known as the recovery problem and it was first studied in [50], see also [45].…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

On stochastic control for time changed Lévy dynamics

Nunno

2022

SeMA

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“…Time-changed semimartingales when the time change is absolutely continuous w.r.t. the Lebesgue measure or when the timechange is a subordinator is well studied in the literature (see, e.g., [KS02,SV17,DNS14,KMK10] for an overview and applications to finance). In this paper, we consider a time-changed Brownian motion to model risky asset prices (M t ) 0≤t≤T , M t := W Λt , where the only assumptions on the time change (Λ t ) 0≤t≤T are that it is a strictly increasing stochastic process and it is independent of the Brownian motion (W t ) 0≤t≤T .…”

Section: Introductionmentioning

confidence: 99%

Utility maximisation and time-change

Nunno¹,

Haferkorn²,

Khedher³

et al. 2019

Preprint

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We consider the problem of maximising expected utility from terminal wealth in a semimartingale setting, where the semimartingale is written as a sum of a time-changed Brownian motion and a finite variation process. To solve this problem, we consider an initial enlargement of filtration and we derive change of variable formulas for stochastic integrals w.r.t. a time-changed Brownian motion. The change of variable formulas allow us to shift the problem to a maximisation problem under the enlarged filtration for models driven by a Brownian motion and a finite variation process. The latter could be solved by using martingale methods. Then applying again the change of variable formula, we derive the optimal strategy for the original problem for a power utility under certain assumptions on the finite variation process of the semimartingale.

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