{"product_id":"exit-problems-for-lzsvy-and-florin-avram-9783039284580","title":"Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics","description":"\u003cp\u003eExit 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).\u003c\/p\u003e\u003cp\u003eMotivated by these considerations, this Special Issue aims to review and push further the state-of-the-art progress on the following topics: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eW, Z formulas for exit problems of the Lévy and diffusion classes (including drawdown problems)\u003c\/li\u003e\n\u003cli\u003eW, Z formulas for quasi-stationary distributions\u003c\/li\u003e\n\u003cli\u003eAsymptotic results\u003c\/li\u003e\n\u003cli\u003eExtensions to random walks, Markov additive processes, omega models, processes with Parisian reflection or absorbtion, processes with state-dependent drift, etc.\u003c\/li\u003e\n\u003cli\u003eOptimal stopping, dividends, real options, etc.\u003c\/li\u003e\n\u003cli\u003eNumeric computation of the scale functions\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Florin Avram\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3039284584\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783039284580\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Mdpi AG\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 06\/29\/2021\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 218\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.48lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.61h x 6.69w x 0.75d","brand":"Florin Avram","offers":[{"title":"Hardcover","offer_id":47200974405887,"sku":"9783039284580","price":63.9,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_bafdcf4b-0f47-409a-b909-9f41b80df26b.jpg?v=1756788460","url":"https:\/\/www.whiterainbookhouse.com\/products\/exit-problems-for-lzsvy-and-florin-avram-9783039284580","provider":"WR Book House","version":"1.0","type":"link"}