ALBERT

Description: In this paper we introduce a deep learning method for pricing and hedging American-style options. It first computes a candidate optimal stopping policy. From there it derives a lower bound for the price. Then it calculates an upper bound, a point estimate and confidence intervals. Finally, it constructs an approximate dynamic hedging strategy. We test the approach on different specifications of a Bermudan max-call option. In all cases it produces highly accurate prices and dynamic hedging strategies with small replication errors.

Description: The state of a population of planktic foraminifers at a certain time reflects multiple processes in the upper ocean, including environmental conditions to which the population was exposed during its growth, the age of the cohorts, and spatiotemporal patchiness. We carried out depth-stratified (0–60, 60–100 m) replicated sampling off Puerto Rico in autumn 2012, revisiting three stations previously sampled in autumn 1994 and spring 1995, in order to analyze seasonal and interannual variability of planktic foraminifers and the stable isotopic composition of their tests. The merged dataset from all three sampling campaigns allows us to assess short- and long-term changes in foraminiferal population dynamics and the spatial assemblage coherency along the shelf edge. All three sample series cover more than 2 weeks during either spring (1995) or autumn (1994, 2012) and include the time of the full moon when reproduction of some surface-dwelling planktic foraminifers has been postulated to take place. Our analyses indicate that interannual variability affected the faunal composition, and both autumn assemblages were characterized by oligotrophic tropical species, dominated by Trilobatus sacculifer and Globigerinoides ruber (white and pink variety). However, G. ruber (white) had a higher abundance in 1994 (37 %) than in 2012 (3.5 %), which may be partially due to increasing sea surface temperatures since the 1990s. Between 60 and 100 m water depth, a different faunal composition with a specific stable oxygen isotope signature provides evidence for the presence of the Subtropical Underwater at the sampling site. Measurements on T. sacculifer sampled in autumn 2012 revealed that test size, calcification and incidence of sac-like chambers continued to increase after full moon, and thus no relation to the synodic lunar reproduction cycle was recognized. During autumn 2012, outer bands of hurricane Sandy passed the Greater Antilles and likely affected the foraminifers. Lower standing stocks of living planktic foraminifers and lower stable carbon isotope values from individuals collected in the mixed layer likely indicate the response to increased rainfall and turbidity in the wake of the hurricane.

Description: Past ocean temperatures and salinities can be approximated from combined stable oxygen isotopes (δ18O) and Mg ∕ Ca measurements in fossil foraminiferal tests with varying success. To further refine this approach, we collected living planktic foraminifers by net sampling and pumping of sea surface water from the Caribbean Sea, the eastern Gulf of Mexico and the Florida Straits. Analyses of δ18O and Mg ∕ Ca in eight living planktic species (Globigerinoides sacculifer, Orbulina universa, Neogloboquadrina dutertrei, Pulleniatina obliquiloculata, Globorotalia menardii, Globorotalia ungulata, Globorotalia truncatulinoides and Globorotalia tumida) were compared to measured in situ properties of the ambient seawater (temperature, salinity and δ18Oseawater) and fossil tests of underlying surface sediments. “Vital effects” such as symbiont activity and test growth cause δ18O disequilibria with respect to the ambient seawater and a large scatter in foraminiferal Mg ∕ Ca. Overall, ocean temperature is the most prominent environmental influence on δ18Ocalcite and Mg ∕ Ca. Enrichment of the heavier 18O isotope in living specimens below the mixed layer and in fossil tests is clearly related to lowered in situ temperatures and gametogenic calcification. Mg ∕ Ca-based temperature estimates of G. sacculifer indicate seasonal maximum accumulation rates on the seafloor in early spring (March) at Caribbean stations and later in the year (May) in the Florida Straits, related to the respective mixed layer temperatures of ∼26 ∘C. Notably, G. sacculifer reveals a weak positive linear relationship between foraminiferal derived δ18Oseawater estimates and both measured in situ δ18Oseawater and salinity. Our results affirm the applicability of existing δ18O and Mg ∕ Ca calibrations for the reconstruction of past ocean temperatures and δ18Oseawater reflecting salinity due to the convincing accordance of proxy data in both living and fossil foraminifers, and in situ environmental parameters. Large vital effects and seasonally varying proxy signals, however, need to be taken into account.

Description: Past ocean temperatures and salinities are successfully approximated from combined stable oxygen isotopes (δ18O) and Mg/Ca measurements in fossil foraminiferal tests. To further refine this approach, we collected living planktic foraminifers by net sampling and pumping of seasurface waters from the Caribbean Sea, the eastern Gulf of Mexico, and Florida Straits. Analyses of δ18O and Mg/Ca in eight living planktic species (Globigerinoides sacculifer, Orbulina universa, Neogloboquadrina dutertrei, Pulleniatina obliquiloculata, Globorotalia menardii, Globorotalia ungulata, Globorotalia truncatulinoides and Globorotalia tumida) were compared to measured in situ properties of the ambient seawater (temperature, salinity and δ18Oseawater) and fossil tests of underlying surface sediments. "Vital effects" such as symbiont activity and test growth cause δ18O disequilibria to the ambient seawater and a large scatter in foraminiferal Mg/Ca. Overall, ocean temperature is the most prominent environmental influence on δ18Ocalcite and Mg/Ca. Enrichment of the heavier δ18 isotope in living specimens below the mixed layer and in fossil tests are clearly related to lowered in situ temperatures and gametogenic calcification. Mg/Ca-based temperature estimates of G. sacculifer indicate seasonal maximum accumulation rates on the seafloor in early spring (March) at Caribbean stations and later in the year (May) in the Florida Straits, related to the respective mixed layer temperatures of ~26°C. Notably, G. sacculifer reveals a positive linear relationship between foraminiferal derived δ18Oseawater estimates and both measured in situ δ18Oseawater and salinity. Our results affirm the applicability of existing δ18O and Mg/Ca calibrations for the reconstruction of past ocean temperatures and δ18Oseawater reflecting salinity due to the convincing accordance of proxy data in both living and fossil foraminifers, and in situ environmental parameters. Large "vital effects" and seasonally varying proxy signals, however, need to be taken into account.