arXiv subjects

Kei Noba

Publications and source records attributed to Kei Noba.

22 records · Page 2Linked to original sources

arXiv2018

Approximation and duality problems of refracted processes

For given two standard processes with no positive jumps, we construct, using the excursion theory, a Markov process whose positive and negative motions have the same law as the two processes. The resulting process is a generalization of Kyprianou--Loeffen's refracted Lévy processes. We discuss approximation problem for our refracted processes coming from Lévy processes by removing small jumps and taking the limit as the removal level tends to zero. We also discuss conditions for refracted processes to have dual processes.

math.PR↗

arXiv2018

Generalized scale functions of standard processes with no positive jumps

As a generalization of scale functions of spectrally negative Lévy processes, we define scale functions of general standard processes with no positive jumps. For this purpose, we utilize excursion measures. Using our new scale functions we study Laplace transforms of hitting times, potential measures and duality.

math.PR↗

arXiv2018

On optimal periodic dividend strategies for Lévy risk processes

In this paper, we revisit the optimal periodic dividend problem, in which dividend payments can only be made at the jump times of an independent Poisson process. In the dual (spectrally positive Lévy) model, recent results have shown the optimality of a periodic barrier strategy, which pays dividends at Poissonian dividend-decision times, if and only if the surplus is above some level. In this paper, we show the optimality of this strategy for a spectrally negative Lévy process whose dual has a completely monotone Lévy density. The optimal strategies and value functions are concisely written in terms of the scale functions. Numerical results are also provided.

math.OC↗

arXiv2017

On optimal periodic dividend and capital injection strategies for spectrally negative Lévy models

De Finetti's optimal dividend problem has recently been extended to the case dividend payments can only be made at Poisson arrival times. This paper considers the version with bail-outs where the surplus must be nonnegative uniformly in time. For a general spectrally negative Lévy model, we show the optimality of a Parisian-classical reflection strategy that pays the excess above a given barrier at each Poisson arrival times and also reflects from below at zero in the classical sense.

math.PR↗