# Fluctuation theory for level-dependent Lévy risk processes

@article{Czarna2017FluctuationTF, title={Fluctuation theory for level-dependent L{\'e}vy risk processes}, author={Irmina Czarna and Jos'e Luis P'erez and Tomasz Rolski and Kazutoshi Yamazaki}, journal={Stochastic Processes and their Applications}, year={2017} }

## 20 Citations

### A Review of First-Passage Theory for the Segerdahl-Tichy Risk Process and Open Problems

- Mathematics
- 2019

Four methods for computing the basic functions of spectrally negative Levy and diffusion processes, based on identifying two “basic” monotone harmonic functions/martingales have been developed are reviewed, with the purpose of drawing attention to connections between them, to underline open problems, and to stimulate further work.

### A Review of First-Passage Theory for the Segerdahl Risk Process and Extensions

- Mathematics
- 2021

The Segerdahl process (Segerdahl (1955)), characterized by exponential claims and affine drift, has drawn a considerable amount of interest—see, for example, (Tichy (1984); Avram and Usabel (2008);…

### The W, Z scale functions kit for first passage problems of spectrally negative Lévy processes, and applications to control problems

- MathematicsESAIM: Probability and Statistics
- 2020

In the last years there appeared a great variety of identities for first passage problems of spectrally negative Lévy processes, which can all be expressed in terms of two “q-harmonic functions” (or…

### The W,Z/ν,δ Paradigm for the First Passage of Strong Markov Processes without Positive Jumps

- MathematicsRisks
- 2019

As is well-known, the benefit of restricting Lévy processes without positive jumps is the “ W , Z scale functions paradigm”, by which the knowledge of the scale functions W , Z extends immediately to…

### Optimality of Impulse Control Problem in Refracted Lévy Model with Parisian Ruin and Transaction Costs

- MathematicsJ. Optim. Theory Appl.
- 2020

This work provides sufficient conditions under which the above described impulse policy is optimal for the impulse control problem and provides new analytical formulae for the Parisian refracted q -scale functions in the case of the linear Brownian motion and the Crámer–Lundberg process with exponential claims.

### Optimality of Impulse Control Problem in Refracted Lévy Model with Parisian Ruin and Transaction Costs

- MathematicsJournal of Optimization Theory and Applications
- 2020

Here, we investigate an optimal dividend problem with transaction costs, in which the surplus process is modeled by a refracted Lévy process and the ruin time is considered with Parisian delay. The…

### How Much We Gain by Surplus-Dependent Premiums—Asymptotic Analysis of Ruin Probability

- MathematicsRisks
- 2021

In this paper, we generate boundary value problems for ruin probabilities of surplus-dependent premium risk processes, under a renewal case scenario, Erlang (2) claim arrivals, and a hypoexponential…

### Unified approach for solving exit problems for additive-increase and multiplicative-decrease processes

- MathematicsJournal of Applied Probability
- 2022

We analyse an additive-increase and multiplicative-decrease (also known as growth–collapse) process that grows linearly in time and that, at Poisson epochs, experiences downward jumps that are…

### General Draw-Down Times for Refracted Spectrally Negative Lévy Processes

- MathematicsMethodology and Computing in Applied Probability
- 2022

In this paper, we prove several results involving a general draw-down time from the running maximum for refracted spectrally negative Lévy processes. Using an approximation method, which is excursion…

### The Gerber-Shiu discounted penalty function: A review from practical perspectives

- MathematicsInsurance: Mathematics and Economics
- 2022

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A symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio is developed.