Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics

• Autore: Avram Florin
• Pubblicazione: Basel, Switzerland, : MDPI - Multidisciplinary Digital Publishing Institute, 2021
• Descrizione fisica: 1 online resource (218 p.)
• Soggetto topico: Mathematics and Science; Research and information: general
• Soggetto non controllato: 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
• Persona (resp. second.): AvramFlorin
• Sommario/riassunto: 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).
• Titolo autorizzato: Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910557372503321
• Lo trovi qui: Univ. Federico II