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Relevant bibliographies by topics / Itô-Lévy process

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Academic literature on the topic 'Itô-Lévy process'

Author: Grafiati

Published: 15 June 2021

Last updated: 17 February 2022

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Journal articles on the topic "Itô-Lévy process"

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Tappe, Stefan. "The Itô Integral with respect to an Infinite Dimensional Lévy Process: A Series Approach." International Journal of Stochastic Analysis 2013 (April 4, 2013): 1–14. http://dx.doi.org/10.1155/2013/703769.

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We present an alternative construction of the infinite dimensional Itô integral with respect to a Hilbert space valued Lévy process. This approach is based on the well-known theory of real-valued stochastic integration, and the respective Itô integral is given by a series of Itô integrals with respect to standard Lévy processes. We also prove that this stochastic integral coincides with the Itô integral that has been developed in the literature.

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DI NUNNO, GIULIA, THILO MEYER-BRANDIS, BERNT ØKSENDAL, and FRANK PROSKE. "MALLIAVIN CALCULUS AND ANTICIPATIVE ITÔ FORMULAE FOR LÉVY PROCESSES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 08, no. 02 (2005): 235–58. http://dx.doi.org/10.1142/s0219025705001950.

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We introduce the forward integral with respect to a pure jump Lévy process and prove an Itô formula for this integral. Then we use Mallivin calculus to establish a relationship between the forward integral and the Skorohod integral and apply this to obtain an Itô formula for the Skorohod integral.

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Tan, Xiaoyu, Shenghong Li, and Shuyi Wang. "Pricing European-Style Options in General Lévy Process with Stochastic Interest Rate." Mathematics 8, no. 5 (2020): 731. http://dx.doi.org/10.3390/math8050731.

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This paper extends the traditional jump-diffusion model to a comprehensive general Lévy process model with the stochastic interest rate for European-style options pricing. By using the Girsanov theorem and Itô formula, we derive the uniform formalized pricing formulas under the equivalent martingale measure. This model contains not only the traditional jump-diffusion model, such as the compound Poisson model, the renewal model, the pure-birth jump-diffusion model, but also the infinite activities Lévy model.

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Riedle, Markus. "Stochastic integration with respect to cylindrical Lévy processes in Hilbert spaces: An L2 approach." Infinite Dimensional Analysis, Quantum Probability and Related Topics 17, no. 01 (2014): 1450008. http://dx.doi.org/10.1142/s0219025714500088.

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In this work stochastic integration with respect to cylindrical Lévy processes with weak second moments is introduced. It is well known that a deterministic Hilbert–Schmidt operator radonifies a cylindrical random variable, i.e. it maps a cylindrical random variable to a classical Hilbert space valued random variable. Our approach is based on a generalisation of this result to the radonification of the cylindrical increments of a cylindrical Lévy process by random Hilbert–Schmidt operators. This generalisation enables us to introduce a Hilbert space valued random variable as the stochastic int

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PRIVAULT, NICOLAS. "SPLITTING OF POISSON NOISE AND LÉVY PROCESSES ON REAL LIE ALGEBRAS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 05, no. 01 (2002): 21–40. http://dx.doi.org/10.1142/s0219025702000699.

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The compensated Poisson noise is expressed as a composite sum (splitting) of creation and annihilation operators, whose probabilistic interpretation relies on time changes. We construct an Itô table for this decomposition and obtain continuous and discrete time realizations of Lévy processes on the finite difference algebra [Formula: see text] and on [Formula: see text], e.g. the space–time dual of the Poisson process (compensated gamma process), and the continuous binomial process.

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JAFARI, HOSSEIN, and GHAZALEH RAHIMI. "SMALL-TIME ASYMPTOTICS IN GEOMETRIC ASIAN OPTIONS FOR A STOCHASTIC VOLATILITY JUMP-DIFFUSION MODEL." International Journal of Theoretical and Applied Finance 22, no. 02 (2019): 1950005. http://dx.doi.org/10.1142/s0219024919500055.

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The aim of this paper is to study the small time to maturity of the behavior of the geometric Asian option price and implied volatility under a general stochastic volatility model with Lévy process. The volatility process does not need to be a diffusion or a Markov process, but the future average volatility in the model is a nonadapted process. An anticipating Itô formula for Lévy process and the decomposition of the price (Hull–White formula) are obtained using the Malliavin calculus techniques. The decomposition formula is applied to find the small-time limit of the geometric Asian option pr

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Zhou, Liuwei, and Zhijie Wang. "Portfolio Strategy of Financial Market with Regime Switching Driven by Geometric Lévy Process." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/538041.

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The problem of a portfolio strategy for financial market with regime switching driven by geometric Lévy process is investigated in this paper. The considered financial market includes one bond and multiple stocks which has few researches up to now. A new and general Black-Scholes (B-S) model is set up, in which the interest rate of the bond, the rate of return, and the volatility of the stocks vary as the market states switching and the stock prices are driven by geometric Lévy process. For the general B-S model of the financial market, a portfolio strategy which is determined by a partial dif

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8

LYTVYNOV, EUGENE. "ORTHOGONAL DECOMPOSITIONS FOR LÉVY PROCESSES WITH AN APPLICATION TO THE GAMMA, PASCAL, AND MEIXNER PROCESSES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 06, no. 01 (2003): 73–102. http://dx.doi.org/10.1142/s0219025703001031.

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It is well known that between all processes with independent increments, essentially only the Brownian motion and the Poisson process possess the chaotic representation property (CRP). Thus, a natural question appears: What is an appropriate analog of the CRP in the case of a general Lévy process. At least three approaches are possible here. The first one, due to Itô, uses the CRP of the Brownian motion and the Poisson process, as well as the representation of a Lévy process through those processes. The second approach, due to Nualart and Schoutens, consists of representing any square-integrab

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9

Øksendal, Bernt, Leif Sandal, and Jan Ubøe. "Stackelberg equilibria in a continuous-time vertical contracting model with uncertain demand and delayed information." Journal of Applied Probability 51, A (2014): 213–26. http://dx.doi.org/10.1017/s002190020002129x.

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We consider explicit formulae for equilibrium prices in a continuous-time vertical contracting model. A manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits. Demand is an Itô-Lévy process, and to increase realism, information is delayed. We provide complete existence and uniqueness proofs for a series of special cases, including geometric Brownian motion and the Ornstein-Uhlenbeck process, both with time-variable coefficients. Moreover, explicit solution formulae are given, so these results are operational. An interesting finding is that inf

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Øksendal, Bernt, Leif Sandal, and Jan Ubøe. "Stackelberg equilibria in a continuous-time vertical contracting model with uncertain demand and delayed information." Journal of Applied Probability 51, A (2014): 213–26. http://dx.doi.org/10.1239/jap/1417528477.

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We consider explicit formulae for equilibrium prices in a continuous-time vertical contracting model. A manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits. Demand is an Itô-Lévy process, and to increase realism, information is delayed. We provide complete existence and uniqueness proofs for a series of special cases, including geometric Brownian motion and the Ornstein-Uhlenbeck process, both with time-variable coefficients. Moreover, explicit solution formulae are given, so these results are operational. An interesting finding is that inf

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Dissertations / Theses on the topic "Itô-Lévy process"

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MBITI, JOHN N. "Deep learning for portfolio optimization." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-104567.

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In this thesis, an optimal investment problem is studied for an investor who can only invest in a financial market modelled by an Itô-Lévy process; with one risk free (bond) and one risky (stock) investment possibility. We present the dynamic programming method and the associated Hamilton-Jacobi-Bellman (HJB) equation to explicitly solve this problem. It is shown that with purification and simplification to the standard jump diffusion process, closed form solutions for the optimal investment strategy and for the value function are attainable. It is also shown that, an explicit solution can be

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Rahouli, Sami El. "Modélisation financière avec des processus de Volterra et applications aux options, aux taux d'intérêt et aux risques de crédit." Thesis, Université de Lorraine, 2014. http://www.theses.fr/2014LORR0042/document.

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Ce travail étudie des modèles financiers pour les prix d'options, les taux d'intérêts et le risque de crédit, avec des processus stochastiques à mémoire et comportant des discontinuités. Ces modèles sont formulés en termes du mouvement Brownien fractionnaire, du processus de Lévy fractionnaire ou filtré (et doublement stochastique) et de leurs approximations par des semimartingales. Leur calcul stochastique est traité au sens de Malliavin, et des formules d'Itô sont déduites. Nous caractérisons les probabilités risque neutre en termes de ces processus pour des modèles d'évaluation d'options de

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Book chapters on the topic "Itô-Lévy process"

1

Kyprianou, Andreas E. "The Lévy–Itô Decomposition and Path Structure." In Fluctuations of Lévy Processes with Applications. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-37632-0_2.

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Aïıt-Sahalia, Yacine, and Jean Jacod. "From Diffusions to Semimartingales." In High-Frequency Financial Econometrics. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691161433.003.0001.

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This chapter presents a quick review of the theory of semimartingales, which are processes for which statistical methods are considered in this book. Topics covered include diffusions, Lévy processes, Itô semimartingales, and processes with conditionally independent increments.

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3

"1. Lévy processes and Itô calculus." In Stochastic Calculus of Variations for Jump Processes. DE GRUYTER, 2013. http://dx.doi.org/10.1515/9783110282009.5.

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