Forward transition rates

The idea of forward rates stems from interest rate theory. It has natural connotations to transition rates in multi-state models. The generalization from the forward mortality rate in a survival model to multi-state models is non-trivial and several definitions have been proposed. We establish a theoretical framework for the discussion of forward rates. Furthermore, we provide a novel definition with its own logic and merits and compare it with the proposals in the literature. The definition turns the Kolmogorov forward equations inside out by interchanging the transition probabilities with the transition intensities as the object to be calculated.Comment: Revision of manuscript. The manuscript now contains a section on 'Forward-thinking and actuarial practice'. Furthermore, we have corrected typos and re-written certain sentences to improve readability and accurac

Obrazovni biblijski nacionalizam i projekt moderne sekularne države

Biblical Criticism, the historical study of Biblical texts, spread across the European universities during the late 19th century, the same period when the European states modernized, and identifying state and nation became a political project. The new scientific view on the Bible became in this political reform context a topic of public debate: Should the national education systems under construction implement the modern scientific understanding of the Bible, should school keep teaching the Catechism, or should religious instruction be separated from the school of the nation in order to become a ‘school for all’? Whereas the academic hotbeds of Biblical Criticism were not least the Germanspeaking universities and academic institutions in France, the popularization of Biblical Criticism through education proved more successful in the Nordic states than in e.g. Prussia and France. The article explores the gradual success of Biblical Criticism education reform efforts in the case of Denmark from the late 19th to mid-20th century in relation to the development of the state from an absolutist kingdom to a nation state with constitutional monarchy and parliamentarism, and discusses on this basis the relation between religion, secularization and educational nation-state crafting.Biblijski kriticizam, tj. povijesno proučavanje biblijskih tekstova, proširio se europskim sveučilištima tijekom kasnog 19. stoljeća, u istom periodu u kojem su se europske države modernizirale, a identifikacija države i nacije postala politički projekt. Neka znanstvena gledišta na Bibliju postala su tema javne rasprave u kontekstu spomenute političke reforme: trebaju li nacionalni obrazovni sustavi u okviru reforme primijeniti moderno znanstveno razumijevanje Biblije; treba li škola nastaviti poučavati katekizam ili bi se poduka religije trebala odvojiti od državne škole da bi postala ‘škola za sve’? Dok su akademska legla biblijskog kriticizma bila posebno sveučilišta na kojima se govorio njemački i akademske institucije u Francuskoj, popularizacija biblijskoga kriticizma kroz obrazovanje bila je uspješnija u nordijskim zemljama nego u npr. Prusiji i Francuskoj. U ovom radu istražuje se postupan uspjeh nastojanja reforme obrazovanja u području biblijskoga kriticizma u slučaju Danske iz perioda kasnog 19. do sredine 20. stoljeća, u odnosu na razvoj države iz apsolutističke kraljevine u nacionalnu državu s konstitucionalnom monarhijom i parlamentarizmom, i na toj osnovi propituje odnos između religije, sekularizacije i obrazovnoga oblikovanja nacionalne države

Hedging and Cash Flows in the Presence of Taxes and Expenses in Life and Pension Insurance

In investment and insurance contracts, certain stipulated payments may depend on the hedging strategy. We study the problem of calculation, hedging and valuation of such cash flows, by considering a payment process in a setup with taxes and investment costs that are functions of the investment returns or the current value of the hedging strategy. We determine the market value of the combined liability and decompose the value into the tax part, the investment cost part and the benefit part, and we determine the associated hedging strategies. Moreover, we identify the expected future tax payments and investment cost cash flows. Our results show that the current Danish insurance accounting practice for taxes is in general conservative, when considered in an idealized setting with symmetric and continuously-paid taxes. Finally, we consider the special case of affine interest rates, where explicit results can be obtained, and study some numerical results

Initial Transgressive Phase of Leg 144 Guyots: Evidence of Extreme Sulfate Reduction

The initial transgressive phase at the Leg 144 Guyots is characterized by a typical association of sedimentary facies (from bottom to top): in situ weathered volcanic rocks; variegated clays, partly pyritic; gray clay, pyritic, homogeneous, or mottled; black clay, peaty, laminated, or bioturbated; and marine argillaceous limestone. Site 877 at Wodejebato Guyot represents the typical development of the initial transgressive phase. The black clay is rich in organic carbon (up to 40%) and sulfur (up to 25%). The organic matter is dominantly of terrestrial origin, but it has a significant marine, algal input. The variegated clays consist of a red, lower, sulfur-free part and a blue to gray-blue, sulfur-containing upper part. Organic carbon is not observed in this facies. The sulfur occurs as pyrite and organically bound sulfur. The isotope composition of pyrite varies from -50‰ to 0%e, which clearly points to bacterial sulfate reduction as the origin for the high sulfur content. Pyrite formation was limited by availability of reactive iron. Because of the origin of the clays as lateritic weathering products, the amount of reactive iron was high, and pyritization proceeded to high values. The following model is suggested for sulfur enrichment in the sediments at the initial transgressive phase: (1) marine flooding of an organic-rich back-reef mangroval swamp; (2) intense bacterial reduction of marine sulfate within the black clay; and (3) downward diffusion of H2S into the underlying clays, reduction of red iron oxides to blue-gray iron sulfides, and growth of pyrite

Tax- and expense-modified risk-minimization for insurance payment processes

We study the problem of determining risk-minimizing investment strategies for insurance payment processes in the presence of taxes and expenses. We consider the situation where taxes and expenses are paid continuously and symmetrically and introduce the concept of tax- and expense-modified risk-minimization. Risk-minimizing strategies in the presence of taxes and expenses are derived and linked to Galtchouk-Kunita-Watanabe decompositions associated with modified versions of the original payment processes. Furthermore, we show equivalence to an alternative approach involving an artificial market consisting of after-tax and after-expense assets, and we establish a type of consistency with classic risk-minimization. Finally, a case study involving classic multi-state life insurance payments in combination with a bond market exemplifies the results