LEADER 04553nam 2201057z- 450 001 9910557372503321 005 20220111 035 $a(CKB)5400000000042166 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/76508 035 $a(oapen)doab76508 035 $a(EXLCZ)995400000000042166 100 $a20202201d2021 |y 0 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aExit Problems for Le?vy and Markov Processes with One-Sided Jumps and Related Topics 210 $aBasel, Switzerland$cMDPI - Multidisciplinary Digital Publishing Institute$d2021 215 $a1 online resource (218 p.) 311 08$a3-03928-458-4 311 08$a3-03928-459-2 330 $aExit problems for one-dimensional Le?vy 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 Le?vy 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, Le?vy processes with omega-state-dependent killing, and certain Le?vy 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 Le?vy and diffusion classes, even for the simplest risk models with state-dependent parameters (say, Ornstein-Uhlenbeck or Feller branching diffusion with phase-type jumps). 606 $aMathematics and Science$2bicssc 606 $aResearch and information: general$2bicssc 610 $aadjustment coefficient 610 $aaffine coefficients 610 $abankruptcy 610 $abarrier strategies 610 $aboundary-value problem 610 $acapital injection constraint 610 $acapital injections 610 $acapital surplus process 610 $acompletely monotone distributions 610 $ade Finetti valuation objective 610 $adiffusion-type process 610 $adividend payment 610 $adividends 610 $adrawdown 610 $adrawdown process 610 $aerror bounds 610 $afirst crossing time 610 $afirst hitting time 610 $afirst passage 610 $afluctuation theory 610 $ageneral tax structure 610 $aheavy tails 610 $ahyperexponential distribution 610 $ahypergeometric functions 610 $ajoint Laplace transform 610 $aLaguerre series 610 $aLaplace transform 610 $aLe?vy processes 610 $alinear diffusions 610 $alog-convexity 610 $alogarithmic asymptotics 610 $anon-random overshoots 610 $anormal reflection 610 $aoptimal control 610 $aoptimal dividends 610 $aPade? approximations 610 $aParisian ruin 610 $aPollaczek-Khinchine formula 610 $apotential measure 610 $aquadratic programming problem 610 $areflected Brownian motion 610 $areflected Le?vy processes 610 $areflection and absorption 610 $aruin probability 610 $arunning maximum and minimum processes 610 $ascale function 610 $ascale functions 610 $aSegerdahl process 610 $askip-free random walks 610 $aSparre Andersen model 610 $aspectrally negative Le?vy process 610 $aspectrally negative Le?vy processes 610 $aspectrally negative Markov process 610 $aspectrally negative process 610 $astochastic control 610 $aTricomi-Weeks Laplace inversion 610 $atwo-dimensional Brownian motion 610 $avariational problem 615 7$aMathematics and Science 615 7$aResearch and information: general 700 $aAvram$b Florin$4edt$01326700 702 $aAvram$b Florin$4oth 906 $aBOOK 912 $a9910557372503321 996 $aExit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics$93037684 997 $aUNINA