04553nam 2201057z- 450 991055737250332120220111(CKB)5400000000042166(oapen)https://directory.doabooks.org/handle/20.500.12854/76508(oapen)doab76508(EXLCZ)99540000000004216620202201d2021 |y 0engurmn|---annantxtrdacontentcrdamediacrrdacarrierExit Problems for Lévy and Markov Processes with One-Sided Jumps and Related TopicsBasel, SwitzerlandMDPI - Multidisciplinary Digital Publishing Institute20211 online 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).Mathematics and SciencebicsscResearch and information: generalbicsscadjustment coefficientaffine coefficientsbankruptcybarrier strategiesboundary-value problemcapital injection constraintcapital injectionscapital surplus processcompletely monotone distributionsde Finetti valuation objectivediffusion-type processdividend paymentdividendsdrawdowndrawdown processerror boundsfirst crossing timefirst hitting timefirst passagefluctuation theorygeneral tax structureheavy tailshyperexponential distributionhypergeometric functionsjoint Laplace transformLaguerre seriesLaplace transformLévy processeslinear diffusionslog-convexitylogarithmic asymptoticsnon-random overshootsnormal reflectionoptimal controloptimal dividendsPadé approximationsParisian ruinPollaczek-Khinchine formulapotential measurequadratic programming problemreflected Brownian motionreflected Lévy processesreflection and absorptionruin probabilityrunning maximum and minimum processesscale functionscale functionsSegerdahl processskip-free random walksSparre Andersen modelspectrally negative Lévy processspectrally negative Lévy processesspectrally negative Markov processspectrally negative processstochastic controlTricomi-Weeks Laplace inversiontwo-dimensional Brownian motionvariational problemMathematics and ScienceResearch and information: generalAvram Florinedt1326700Avram FlorinothBOOK9910557372503321Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics3037684UNINA