Feynman path integrals and asymptotic expansions for transition probability densities of some Lévy driven financial markets

Issaka, Aziz; Sengupta, Indranil

doi:10.1007/s12190-016-1002-2

Cited by 9 publications

(1 citation statement)

References 18 publications

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“…Functions with similar series expansions are also involved in the study of the asymptotic behaviour of some integrals, which arise from a Feynman path integral approach to some financial problems (see, i.e., [25] Section 4). Recall also the following Laplace transform formula [9] L[z γ−1 E δ ν,γ (wz ν )](s) = s νδ−γ (s ν − w) δ , γ, ν, δ, w ∈ C, (γ), (ν), (δ) > 0, s ∈ C, |ws ν | < 1.…”

Section: Appendix a Fractional Integrals And Derivativesmentioning

confidence: 99%

Fractional Queues with Catastrophes and Their Transient Behaviour

2018

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Starting from the definition of fractional M/M/1 queue given in the reference by Cahoy et al. in 2015 and M/M/1 queue with catastrophes given in the reference by Di Crescenzo et al. in 2003, we define and study a fractional M/M/1 queue with catastrophes. In particular, we focus our attention on the transient behaviour, in which the time-change plays a key role. We first specify the conditions for the global uniqueness of solutions of the corresponding linear fractional differential problem. Then, we provide an alternative expression for the transient distribution of the fractional M/M/1 model, the state probabilities for the fractional queue with catastrophes, the distributions of the busy period for fractional queues without and with catastrophes and, finally, the distribution of the time of the first occurrence of a catastrophe.

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Section: Appendix a Fractional Integrals And Derivativesmentioning

confidence: 99%

Fractional Queues with Catastrophes and Their Transient Behaviour

2018

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Refinements of Barndorff-Nielsen and Shephard Model: An Analysis of Crude Oil Price with Machine Learning

2020

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A commonly used stochastic model for derivative and commodity market analysis is the Barndorff-Nielsen and Shephard (BN-S) model. Though this model is very efficient and analytically tractable, it suffers from the absence of long range dependence and many other issues. For this paper, the analysis is restricted to crude oil price dynamics. A simple way of improving the BN-S model with the implementation of various machine learning algorithms is proposed. This refined BN-S model is more efficient and has fewer parameters than other models which are used in practice as improvements of the BN-S model. The procedure and the model show the application of data science for extracting a "deterministic component" out of processes that are usually considered to be completely stochastic. Empirical applications validate the efficacy of the proposed model for long range dependence.

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