04523nam 2201045z- 450 991055737250332120231214132959.0(CKB)5400000000042166(oapen)https://directory.doabooks.org/handle/20.500.12854/76508(EXLCZ)99540000000004216620202201d2021 |y 0engurmn|---annantxtrdacontentcrdamediacrrdacarrierExit Problems for Lévy and Markov Processes with One-Sided Jumps and Related TopicsBasel, SwitzerlandMDPI - Multidisciplinary Digital Publishing Institute20211 electronic resource (218 p.)3-03928-458-4 3-03928-459-2 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).Research & information: generalbicsscMathematics & sciencebicsscLévy processesnon-random overshootsskip-free random walksfluctuation theoryscale functionscapital surplus processdividend paymentoptimal controlcapital injection constraintspectrally negative Lévy processesreflected Lévy processesfirst passagedrawdown processspectrally negative processdividendsde Finetti valuation objectivevariational problemstochastic controloptimal dividendsParisian ruinlog-convexitybarrier strategiesadjustment coefficientlogarithmic asymptoticsquadratic programming problemruin probabilitytwo-dimensional Brownian motionspectrally negative Lévy processgeneral tax structurefirst crossing timejoint Laplace transformpotential measureLaplace transformfirst hitting timediffusion-type processrunning maximum and minimum processesboundary-value problemnormal reflectionSparre Andersen modelheavy tailscompletely monotone distributionserror boundshyperexponential distributionreflected Brownian motionlinear diffusionsdrawdownSegerdahl processaffine coefficientsspectrally negative Markov processhypergeometric functionscapital injectionsbankruptcyreflection and absorptionPollaczek–Khinchine formulascale functionPadé approximationsLaguerre seriesTricomi–Weeks Laplace inversionResearch & information: generalMathematics & scienceAvram Florinedt1326700Avram FlorinothBOOK9910557372503321Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics3037684UNINA