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Relevant bibliographies by topics / Running supremum

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Journal articles

Academic literature on the topic 'Running supremum'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Running supremum"

1

Carvajal Pinto, Mónica B., and Kees van Schaik. "Optimally Stopping at a Given Distance from the Ultimate Supremum of a Spectrally Negative Lévy Process." Advances in Applied Probability 53, no. 1 (2021): 279–99. http://dx.doi.org/10.1017/apr.2020.54.

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AbstractWe consider the optimal prediction problem of stopping a spectrally negative Lévy process as close as possible to a given distance $b \geq 0$ from its ultimate supremum, under a squared-error penalty function. Under some mild conditions, the solution is fully and explicitly characterised in terms of scale functions. We find that the solution has an interesting non-trivial structure: if b is larger than a certain threshold then it is optimal to stop as soon as the difference between the running supremum and the position of the process exceeds a certain level (less than b), while if b is

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2

Coutin, Laure, Monique Pontier, and Waly Ngom. "Joint distribution of a Lévy process and its running supremum." Journal of Applied Probability 55, no. 2 (2018): 488–512. http://dx.doi.org/10.1017/jpr.2018.32.

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Abstract Let X be a jump-diffusion process and X* its running supremum. In this paper we first show that for any t > 0, the law of the pair (X*t, Xt) has a density with respect to the Lebesgue measure. This allows us to show that for any t > 0, the law of the pair formed by the random variable Xt and the running supremum X*t of X at time t can be characterized as a weak solution of a partial differential equation concerning the distribution of the pair (X*t, Xt). Then we obtain an expression of the marginal density of X*t for all t > 0.

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3

Kyprianou, Andreas E., and Curdin Ott. "Spectrally Negative Lévy Processes Perturbed by Functionals of their Running Supremum." Journal of Applied Probability 49, no. 04 (2012): 1005–14. http://dx.doi.org/10.1017/s0021900200012845.

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In the setting of the classical Cramér–Lundberg risk insurance model, Albrecher and Hipp (2007) introduced the idea of tax payments. More precisely, if X = {X t : t≥ 0} represents the Cramér–Lundberg process and, for all t≥ 0, S t =sup_{s≤ t}X s , then Albrecher and Hipp studied X t - γ S t ,t≥ 0, where γ∈(0,1) is the rate at which tax is paid. This model has been generalised to the setting that X is a spectrally negative Lévy process by Albrecher, Renaud and Zhou (2008). Finally, Kyprianou and Zhou (2009) extended this model further by allowing the rate at which tax is paid with respect to th

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4

Kyprianou, Andreas E., and Curdin Ott. "Spectrally Negative Lévy Processes Perturbed by Functionals of their Running Supremum." Journal of Applied Probability 49, no. 4 (2012): 1005–14. http://dx.doi.org/10.1239/jap/1354716654.

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In the setting of the classical Cramér–Lundberg risk insurance model, Albrecher and Hipp (2007) introduced the idea of tax payments. More precisely, if X = {Xt: t≥ 0} represents the Cramér–Lundberg process and, for all t≥ 0, St=sup_{s≤ t}Xs, then Albrecher and Hipp studied Xt - γ St,t≥ 0, where γ∈(0,1) is the rate at which tax is paid. This model has been generalised to the setting that X is a spectrally negative Lévy process by Albrecher, Renaud and Zhou (2008). Finally, Kyprianou and Zhou (2009) extended this model further by allowing the rate at which tax is paid with respect to the process

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5

Blanchet-Scalliet, Christophette, Diana Dorobantu, and Laura Gay. "Joint law of an Ornstein–Uhlenbeck process and its supremum." Journal of Applied Probability 57, no. 2 (2020): 541–58. http://dx.doi.org/10.1017/jpr.2020.22.

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AbstractLet X be an Ornstein–Uhlenbeck process driven by a Brownian motion. We propose an expression for the joint density / distribution function of the process and its running supremum. This law is expressed as an expansion involving parabolic cylinder functions. Numerically, we obtain this law faster with our expression than with a Monte Carlo method. Numerical applications illustrate the interest of this result.

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6

Ferreiro-Castilla, Albert, and Kees van Schaik. "Applying the Wiener-Hopf Monte Carlo Simulation Technique for Lévy Processes to Path Functionals." Journal of Applied Probability 52, no. 01 (2015): 129–48. http://dx.doi.org/10.1017/s0021900200012249.

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In this paper we apply the recently established Wiener-Hopf Monte Carlo simulation technique for Lévy processes from Kuznetsov et al. (2011) to path functionals; in particular, first passage times, overshoots, undershoots, and the last maximum before the passage time. Such functionals have many applications, for instance, in finance (the pricing of exotic options in a Lévy model) and insurance (ruin time, debt at ruin, and related quantities for a Lévy insurance risk process). The technique works for any Lévy process whose running infimum and supremum evaluated at an independent exponential ti

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7

Ferreiro-Castilla, Albert, and Kees van Schaik. "Applying the Wiener-Hopf Monte Carlo Simulation Technique for Lévy Processes to Path Functionals." Journal of Applied Probability 52, no. 1 (2015): 129–48. http://dx.doi.org/10.1239/jap/1429282611.

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In this paper we apply the recently established Wiener-Hopf Monte Carlo simulation technique for Lévy processes from Kuznetsov et al. (2011) to path functionals; in particular, first passage times, overshoots, undershoots, and the last maximum before the passage time. Such functionals have many applications, for instance, in finance (the pricing of exotic options in a Lévy model) and insurance (ruin time, debt at ruin, and related quantities for a Lévy insurance risk process). The technique works for any Lévy process whose running infimum and supremum evaluated at an independent exponential ti

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8

Kyprianou, Andreas E., Victor Rivero, and Weerapat Satitkanitkul. "Deep Factorisation of the Stable Process III: the View from Radial Excursion Theory and the Point of Closest Reach." Potential Analysis 53, no. 4 (2019): 1347–75. http://dx.doi.org/10.1007/s11118-019-09809-4.

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AbstractWe compute explicitly the distribution of the point of closest reach to the origin in the path of any d-dimensional isotropic stable process, with d ≥ 2. Moreover, we develop a new radial excursion theory, from which we push the classical Blumenthal–Getoor–Ray identities for first entry/exit into a ball (cf. Blumenthal et al. Trans. Amer. Math. Soc., 99, 540–554 1961) into the more complex setting of n-tuple laws for overshoots and undershoots. We identify explicitly the stationary distribution of any d-dimensional isotropic stable process when reflected in its running radial supremum.

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9

Herzberg, Anne. "Kiobel and Corporate Complicity– Running with the Pack." AJIL Unbound 107 (2013): 41–48. http://dx.doi.org/10.1017/s2398772300009685.

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Many human rights activists have lamented the outcome of Kiobel v. Royal Dutch Petroleum Co. Reacting to the opinion, Human Rights Watch expressed concern that Kiobel “significantly reduce[s] the possibility that corporations can be held accountable in US courts for human rights abuses committed abroad.” The Center for Constitutional Rights issued a statement that it was “deeply troubled by the Supreme Court's decision to undercut 30 years of jurisprudence.”

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10

Bleemer, Russ. "Supreme court will address long-running battles over arbitration review." Alternatives to the High Cost of Litigation 25, no. 7 (2007): 119–23. http://dx.doi.org/10.1002/alt.20190.

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