A soft robust model for optimization under ambiguity

In this paper, we propose a framework for robust optimization that relaxes the standard notion of robustness by allowing the decision maker to vary the protection level in a smooth way across the uncertainty set. We apply our approach to the problem of maximizing the expected value of a payoff function when the underlying distribution is ambiguous and therefore robustness is relevant. Our primary objective is to develop this framework and relate it to the standard notion of robustness, which deals with only a single guarantee across one uncertainty set. First, we show that our approach connects closely to the theory of convex risk measures. We show that the complexity of this approach is equivalent to that of solving a small number of standard robust problems. We then investigate the conservatism benefits and downside probability guarantees implied by this approach and compare to the standard robust approach. Finally, we illustrate theme thodology on an asset allocation example consisting of historical market data over a 25-year investment horizon and find in every case we explore that relaxing standard robustness with soft robustness yields a seemingly favorable risk-return trade-off: each case results in a higher out-of-sample expected return for a relatively minor degradation of out-of-sample downside performance. © 2010 INFORMS.

Biological and Physical Factors Affecting the Natural History and Evolution of Encapsulated Development

The evolution of reproductive strategies involves a complex calculus of costs and benefits to both parents and offspring. Many marine animals produce embryos packaged in tough egg capsules or gelatinous egg masses attached to benthic surfaces. While these egg structures can protect against environmental stresses, the packaging is energetically costly for parents to produce. In this series of studies, I examined a variety of ecological factors affecting the evolution of benthic development as a life history strategy. I used marine gastropods as my model system because they are incredibly diverse and abundant worldwide, and they exhibit a variety of reproductive and developmental strategies.

The first study examines predation on benthic egg masses. I investigated: 1) behavioral mechanisms of predation when embryos are targeted (rather than the whole egg mass); 2) the specific role of gelatinous matrix in predation. I hypothesized that gelatinous matrix does not facilitate predation. One study system was the sea slug Olea hansineensis, an obligate egg mass predator, feeding on the sea slug Haminoea vesicula. Olea fed intensely and efficiently on individual Haminoea embryos inside egg masses but showed no response to live embryos removed from gel, suggesting that gelatinous matrix enables predation. This may be due to mechanical support of the feeding predator by the matrix. However, Haminoea egg masses outnumber Olea by two orders of magnitude in the field, and each egg mass can contain many tens of thousands of embryos, so predation pressure on individuals is likely not strong. The second system involved the snail Nassarius vibex, a non-obligate egg mass predator, feeding on the polychaete worm Clymenella mucosa. Gel neither inhibits nor promotes embryo predation for Nassarius, but because it cannot target individual embryos inside an egg mass, its feeding is slow and inefficient, and feeding rates in the field are quite low. However, snails that compete with Nassarius for scavenged food have not been seen to eat egg masses in the field, leaving Nassarius free to exploit the resource. Overall, egg mass predation in these two systems likely benefits the predators much more than it negatively affects the prey. Thus, selection for environmentally protective aspects of egg mass production may be much stronger than selection for defense against predation.

In the second study, I examined desiccation resistance in intertidal egg masses made by Haminoea vesicula, which preferentially attaches its flat, ribbon-shaped egg masses to submerged substrata. Egg masses occasionally detach and become stranded on exposed sand at low tide. Unlike adults, the encased embryos cannot avoid desiccation by selectively moving about the habitat, and the egg mass shape has high surface-area-to-volume ratio that should make it prone to drying out. Thus, I hypothesized that the embryos would not survive stranding. I tested this by deploying individual egg masses of two age classes on exposed sand bars for the duration of low tide. After rehydration, embryos midway through development showed higher rates of survival than newly-laid embryos, though for both stages survival rates over 25% were frequently observed. Laboratory desiccation trials showed that >75% survival is possible in an egg mass that has lost 65% of its water weight, and some survival (<25%) was observed even after 83% water weight lost. Although many surviving embryos in both experiments showed damage, these data demonstrate that egg mass stranding is not necessarily fatal to embryos. They may be able to survive a far greater range of conditions than they normally encounter, compensating for their lack of ability to move. Also, desiccation tolerance of embryos may reduce pressure on parents to find optimal laying substrata.

The third study takes a big-picture approach to investigating the evolution of different developmental strategies in cone snails, the largest genus of marine invertebrates. Cone snail species hatch out of their capsules as either swimming larvae or non-dispersing forms, and their developmental mode has direct consequences for biogeographic patterns. Variability in life history strategies among taxa may be influenced by biological, environmental, or phylogenetic factors, or a combination of these. While most prior research has examined these factors singularly, my aim was to investigate the effects of a host of intrinsic, extrinsic, and historical factors on two fundamental aspects of life history: egg size and egg number. I used phylogenetic generalized least-squares regression models to examine relationships between these two egg traits and a variety of hypothesized intrinsic and extrinsic variables. Adult shell morphology and spatial variability in productivity and salinity across a species geographic range had the strongest effects on egg diameter and number of eggs per capsule. Phylogeny had no significant influence. Developmental mode in Conus appears to be influenced mostly by species-level adaptations and niche specificity rather than phylogenetic conservatism. Patterns of egg size and egg number appear to reflect energetic tradeoffs with body size and specific morphologies as well as adaptations to variable environments. Overall, this series of studies highlights the importance of organism-scale biotic and abiotic interactions in evolutionary patterns.

Optimal Reporting Systems With Investor Information Acquisition

This paper analyzes a manager's optimal ex-ante reporting system using a Bayesian persuasion approach (Kamenica and Gentzkow (2011)) in a setting where investors affect cash flows through their decision to finance the firm's investment opportunities, possibly assisted by the costly acquisition of additional information (inspection). I examine how the informativeness and the bias of the optimal system are determined by investors' inspection cost, the degree of incentive alignment between the manager and the investor, and the prior belief that the project is profitable. I find that a mis-aligned manager's system is informative

only when the market prior is pessimistic and is always positively biased; this bias decreases as investors' inspection cost decreases. In contrast, a well-aligned manager's system is fully revealing when investors' inspection cost is high, and is counter-cyclical to the market belief when the inspection cost is low: It is positively (negatively) biased when the market belief is pessimistic (optimistic). Furthermore, I explore the extent to which the results generalize to a case with managerial manipulation and discuss the implications for investment efficiency. Overall, the analysis describes the complex interactions among determinants of firm disclosures and governance, and offers explanations for the mixed empirical results in this area.