Singular recursive utility

We introduce the concept of singular recursive utility. This leads to a kind of singular BSDE which, to the best of our knowledge, has not been studied before. We show conditions for existence and uniqueness of a solution for this kind of singular BSDE. Furthermore, we analyze the problem of maximizing the singular recursive utility. We derive sufficient and necessary maximum principles for this problem, and connect it to the Skorohod reflection problem. Finally, we apply our results to a specific cash flow. In this case, we find that the optimal consumption rate is given by the solution to the corresponding Skorohod reflection problem

A duopoly preemption game with two alternative stochastic investment choices

This paper studies a duopoly investment model with uncertainty. There are two alternative irreversible investments. The first firm to invest gets a monopoly benefit for a specified period of time. The second firm to invest gets information based on what happens with the first investor, as well as cost reduction benefits. We describe the payoff functions for both the leader and follower firm. Then, we present a stochastic control game where the firms can choose when to invest, and hence influence whether they become the leader or the follower. In order to solve this problem, we combine techniques from optimal stopping and game theory. For a specific choice of parametres, we show that no pure symmetric subgame perfect Nash equilibrium exists. However, an asymmetric equilibrium is characterized. In this equilibrium, two disjoint intervals of market demand level give rise to preemptive investment behavior of the firms, while the firms otherwise are more reluctant to be the first mover

Tropical climate variability from the last glacial maximum to the present

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September, 2005This thesis evaluates the nature and magnitude of tropical climate variability from the Last Glacial Maximum to the present. The temporal variability of two specific tropical climate phenomena is examined. The first is the position of the Intertropical Convergence Zone (ITCZ) in the Atlantic basin, which affects sea surface temperature (SST) and precipitation patterns throughout the tropical Atlantic. The second is the strength of the Indian Monsoon, an important component of both tropical and global climate. Long-term variations in the position of the ITCZ in the Atlantic region are determined using both organic geochemical techniques and climate modeling. Upwelling in Cariaco Basin is reconstructed using chlorin steryl esters as proxies for phytoplankton community structure. We find that the diatom population was larger during the Younger Dryas cold event, indicating that upwelling was enhanced and the mean position of the ITCZ was farther south during the Younger Dryas than it is today. A climate simulation using an ocean-atmosphere general circulation model confirms these results by demonstrating that the ITCZ shifts southward in response to high-latitude cooling. The climate of the Arabian Sea region is dominated by the Indian Monsoon. Results from modem sediments from a suite of cores located throughout the Arabian Sea suggest that wind strength is well represented by the accumulation rate and carbon isotopic composition of terrestrially-derived plant waxes in sediments. Arabian Sea SST patterns, reconstructed from a suite of sediment cores representing four time slices utilizing the Mg/Ca SST proxy, suggest that both the summer and winter monsoons were enhanced 8,000 yr BP relative to today while the summer monsoon was weaker and the winter monsoon stronger at 15,000 and 20,000 yr. These results are confirmed by a time-series reconstruction of SST on the Oman Margin that reveals that SST at this site is sensitive to both regional and global climate processes. The results of this thesis demonstrate that tropical climate, as evaluated by a number of different proxies as well as climate models, has varied substantially over the past 20,000 years and is closely coupled to climate at high-latitudes.This work was funded by the National Science Foundation (OCE02-20776 and OCE0334598 to D. Oppo), a Schlanger Ocean Drilling Program Fellowship, a WHOI Watson Fellowship, and a Fye Teaching Fellowship