Discounted penalty function at Parisian ruin for Lévy insurance risk process

R Loeffen, Z Palmowski, BA Surya - Insurance: Mathematics and …, 2018 - Elsevier
In the setting of a Lévy insurance risk process, we present some results regarding the
Parisian ruin problem which concerns the occurrence of an excursion below zero of duration …

[HTML][HTML] Spectrally negative Lévy processes with Parisian reflection below and classical reflection above

F Avram, JL Pérez, K Yamazaki - Stochastic Processes and their …, 2018 - Elsevier
We consider a company that receives capital injections so as to avoid ruin. Differently from
the classical bail-out settings, where the underlying process is restricted to stay at or above …

On the distribution of cumulative Parisian ruin

H Guérin, JF Renaud - Insurance: Mathematics and Economics, 2017 - Elsevier
We introduce the concept of cumulative Parisian ruin, which is based on the time spent in
the red by the underlying surplus process. Our main result is an explicit representation for …

Parisian ruin for a refracted Lévy process

MA Lkabous, I Czarna, JF Renaud - Insurance: Mathematics and …, 2017 - Elsevier
In this paper, we investigate Parisian ruin for a Lévy surplus process with an adaptive
premium rate, namely a refracted Lévy process. Our main contribution is a generalization of …

On series expansions for scale functions and other ruin-related quantities

D Landriault, GE Willmot - Scandinavian Actuarial Journal, 2020 - Taylor & Francis
In this note, we consider a nonstandard analytic approach to the examination of scale
functions in some special cases of spectrally negative Lévy processes. In particular, we …

Parisian types of ruin probabilities for a class of dependent risk-reserve processes

M Bladt, BF Nielsen, O Peralta - Scandinavian Actuarial Journal, 2019 - Taylor & Francis
For a rather general class of risk-reserve processes, we provide an exact method for
calculating different kinds of ruin probabilities, with particular emphasis on variations over …

The Leland–Toft optimal capital structure model under Poisson observations

Z Palmowski, JL Pérez, BA Surya, K Yamazaki - Finance and Stochastics, 2020 - Springer
This paper revisits the optimal capital structure model with endogenous bankruptcy, first
studied by Leland (J. Finance 49: 1213–1252, 1994) and Leland and Toft (J. Finance 51 …

On occupation times in the red of Lévy risk models

D Landriault, B Li, MA Lkabous - Insurance: Mathematics and Economics, 2020 - Elsevier
In this paper, we obtain analytical expression for the distribution of the occupation time in the
red (below level 0) up to an (independent) exponential horizon for spectrally negative Lévy …

On the area in the red of Lévy risk processes and related quantities

MA Lkabous, Z Wang - Insurance: Mathematics and Economics, 2023 - Elsevier
Under contemporary insurance regulatory frameworks, an insolvent insurer placed in
receivership may have the option of rehabilitation, during which a plan is devised to resolve …

The Parisian and ultimate drawdowns of Lévy insurance models

S Li, X Zhou - Insurance: Mathematics and Economics, 2022 - Elsevier
In this paper, inspired by the ideas of Parisian ruin and ultimate bankruptcy, we introduce
two new stopping times for the (general) drawdown process, namely, the Parisian drawdown …