Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics
Material type: ArticleLanguage: English Publication details: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2021Description: 1 electronic resource (218 p.)Content type:- text
- computer
- online resource
- 9783039284580
- 9783039284597
- Информационные технологии
- Lévy processes
- non-random overshoots
- skip-free random walks
- fluctuation theory
- scale functions
- capital surplus process
- dividend payment
- optimal control
- capital injection constraint
- spectrally negative Lévy processes
- reflected Lévy processes
- first passage
- drawdown process
- spectrally negative process
- dividends
- de Finetti valuation objective
- variational problem
- stochastic control
- optimal dividends
- Parisian ruin
- log-convexity
- barrier strategies
- adjustment coefficient
- logarithmic asymptotics
- quadratic programming problem
- ruin probability
- two-dimensional Brownian motion
- spectrally negative Lévy process
- general tax structure
- first crossing time
- joint Laplace transform
- potential measure
- Laplace transform
- first hitting time
- diffusion-type process
- running maximum and minimum processes
- boundary-value problem
- normal reflection
- Sparre Andersen model
- heavy tails
- completely monotone distributions
- error bounds
- hyperexponential distribution
- reflected Brownian motion
- linear diffusions
- drawdown
- Segerdahl process
- affine coefficients
- spectrally negative Markov process
- hypergeometric functions
- capital injections
- bankruptcy
- reflection and absorption
- Pollaczek–Khinchine formula
- scale function
- Padé approximations
- Laguerre series
- Tricomi–Weeks Laplace inversion
Item type | Current library | Collection | Shelving location | Call number | Status | Notes | Date due | Barcode |
---|---|---|---|---|---|---|---|---|
Electronic edition | Bucheon University Library | Computers | MDPI books | 004 E97 | Not for loan | View(pdf) | 1011006 |
Open Access star Unrestricted online access
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).
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