Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics
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| Author: |
Avram Florin
|
| Title: |
Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics
|
| Publisher: | Basel, Switzerland, : MDPI - Multidisciplinary Digital Publishing Institute, 2021 |
| Physical description: | 1 online resource (218 p.) |
| Topical subject: | Mathematics and Science |
| Research and information: general | |
| Uncontrolled subject: | adjustment coefficient |
| affine coefficients | |
| bankruptcy | |
| barrier strategies | |
| boundary-value problem | |
| capital injection constraint | |
| capital injections | |
| capital surplus process | |
| completely monotone distributions | |
| de Finetti valuation objective | |
| diffusion-type process | |
| dividend payment | |
| dividends | |
| drawdown | |
| drawdown process | |
| error bounds | |
| first crossing time | |
| first hitting time | |
| first passage | |
| fluctuation theory | |
| general tax structure | |
| heavy tails | |
| hyperexponential distribution | |
| hypergeometric functions | |
| joint Laplace transform | |
| Laguerre series | |
| Laplace transform | |
| Lévy processes | |
| linear diffusions | |
| log-convexity | |
| logarithmic asymptotics | |
| non-random overshoots | |
| normal reflection | |
| optimal control | |
| optimal dividends | |
| Padé approximations | |
| Parisian ruin | |
| Pollaczek-Khinchine formula | |
| potential measure | |
| quadratic programming problem | |
| reflected Brownian motion | |
| reflected Lévy processes | |
| reflection and absorption | |
| ruin probability | |
| running maximum and minimum processes | |
| scale function | |
| scale functions | |
| Segerdahl process | |
| skip-free random walks | |
| Sparre Andersen model | |
| spectrally negative Lévy process | |
| spectrally negative Lévy processes | |
| spectrally negative Markov process | |
| spectrally negative process | |
| stochastic control | |
| Tricomi-Weeks Laplace inversion | |
| two-dimensional Brownian motion | |
| variational problem | |
| Person (second resp.): | AvramFlorin |
| Summary, etc: | Exit problems for one-dimensional Lévy processes are easier when jumps only occur in one direction. In the last few years, this intuition became more precise: we know now that a wide variety of identities for exit problems of spectrally-negative Lévy processes may be ergonomically expressed in terms of two q-harmonic functions (or scale functions or positive martingales) W and Z. The proofs typically require not much more than the strong Markov property, which hold, in principle, for the wider class of spectrally-negative strong Markov processes. This has been established already in particular cases, such as random walks, Markov additive processes, Lévy processes with omega-state-dependent killing, and certain Lévy processes with state dependent drift, and seems to be true for general strong Markov processes, subject to technical conditions. However, computing the functions W and Z is still an open problem outside the Lévy and diffusion classes, even for the simplest risk models with state-dependent parameters (say, Ornstein-Uhlenbeck or Feller branching diffusion with phase-type jumps). |
| Preferred title for the work: | Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics |
| Format: | Language material  |
| Bibliographic level | Monograph |
| Language: | English |
| Record Nr.: | 9910557372503321 |
| You will find it: | Univ. Federico II |
| Opac: | Check copies here |