Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics
Material type:![Article](/opac-tmpl/lib/famfamfam/AR.png)
- books978-3-03928-459-7
- 9783039284580
- 9783039284597
- Research & information: general
- Mathematics & science
- 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 | Home library | Collection | Call number | Materials specified | Status | Date due | Barcode | |
---|---|---|---|---|---|---|---|---|
![]() |
OPJGU Sonepat- Campus | E-Books Open Access | Available |
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).
Creative Commons https://creativecommons.org/licenses/by/4.0/ cc https://creativecommons.org/licenses/by/4.0/
English
There are no comments on this title.