ABSTRACTS

Svetlana Boyarchenko, University of Texas at Austin
“Long-term environmental problems: costly commitments and discounting”

The paper considers a small economy under economic and environmental uncertainty. The economic uncertainty follows a geometric Levy process, while the environmental uncertainty is reflected in a random date of a catastrophe. The catastrophe is exogenous is the sense that it cannot be prevented because the country is small, however, to reduce an impact of the environmental disaster, an unpopular costly abatement policy can be adopted. We demonstrate that (a) if the discount factor for losses is sufficiently large then abatement is never optimal; (b) strong action on climate change requires discount factor for losses to be sufficiently small; (c) improved assessment of the random date of climate catastrophe may delay adoption of abatement programs.

Richard Law, University of York “Dynamics and decisions at the interface of ecology, economics and social behavior”

This talk is concerned with ecological (self-renewing) resources shared by multiple exploiters, the income from these resources, and social interactions among the exploiters. This stems from a personal view that we need to work across the boundaries of ecology, economics and the social sciences, to learn how use self-renewing resources in a sustainable way.

To develop the argument I will describe a simple model of the ecological commons, in which users of the commons change their exploitation rates in an adaptive way to increase their income. Given a fast logistic dynamic for the resource, and no more than the rational (asocial) man of economics, there is no tragedy. However, income from the resource is increased by exploiters who interact with each other to give some weight to the income of other users. The maximum sustainable yield is reached when users of the resource place as much value the income of others as much as their own.

It seems likely that such beneficial social behaviour would disappear if the users are not fully agreed on the weight to give to the income of others. I will give some preliminary results on what happens when a user with a different social behaviour appears.

Sergei Levendorskii, University of Leicester “No-remorse principles for real options”

We give short proofs of general theorems about optimal entry and exit problems n Levy models, when payoff streams may have discontinuities and be non-monotone. As applications, we consider exit and entry problems in the theory of real options, entry problem with an embedded option to exit, and problems with ambiguity and strategic interactions. We demonstrate a non-trivial impact of jump uncertainty and ambiguity on the investment threshold.

Charles F. Mason, University of Wyoming “Designing Carbon Policy With a Stochastically Evolving Climate”

I investigate two assumptions that economic analyses of climate policies commonly impose, either explicitly or implicitly: that damages are linked directly to carbon stocks, and that climate evolves either deterministically or via a relatively simple stochastic process. It has recently been argued that climate, as proxied by temperature, is related to carbon stocks via a differential equation (so that climate is not directly linked to carbon stocks). Accordingly, it is the rate of change – as opposed to the level of – optimal carbon emissions that is related to climate. With respect to the evolution of climate, I present evidence that a more complicated process than Brownian motion (in either levels or logs) is appropriate. Implications for optimal policy are discussed, with particular relation to the recent interest within the literature regarding “fat tails” in the distribution over climate profiles.

Paul Monks, University of Leicester
“Linking Earth Observation Data to Financial Futures”

We live in an era were observation of the earth system from ground, air and space has given us an unprecedented view. In particular, space based observations available through the flagship EU GMES program will herald long-term self-consistent view of global change. GMES (Global Monitoring for Environment and Security) represents a concerted effort to bring data and information providers together, to make environmental and security-related information available to the people who need it through enhanced or new services. The GMES programme applies data from satellite, aerial and ground-based earth observation to information and decision-making products and services.

The talk looked a taking Earth Observation (EO) data and mapping it through to economic impact. It is clear, for example that Earth observation data are ideally suited to the evaluation of risk owing to their high temporal and spatial resolution which can be exploited to evaluate for example in relation to food security crop states and crop yield based upon measurements of several different indicators. Further examples of flood risk using the example of the Tewksbury flood of July 2007 and subsidence measured from space were explored as examples of the utility of EO. The final question explored in the talk is how you take this data and develop through to trading and financial future systems. A case study of agricultural monitoring was explored from the EO observations through to crop yield and financial impact. It is clear that there is potential in this area that required genuine interdisciplinary working from the EO data through products to economic models. A pathway exists but a challenge remains.

Eric Naevdal , University of Oslo
“Economic management of threshold effects in natural resource systems”

The role of discounting in the management of climate change is a hotly debated issue. Many scientists and laymen concerned with potentially catastrophic impacts feel that if an increase in the discount rate drastically increases the likelihood of catastrophic outcomes, this discredits economic cost-benefit calculations. This paper argues that this intuition is sound. If cost-benefit calculations are done within a model that encompasses the type of catastrophic threshold effects that these scientists worry about, the resulting stabilization target will only be slightly influenced by the discount rate.

Sergei Petrovskiy, University of Leicester
“Biological invasion and biological control: Implications for pest management and greener investment”

Biological invasions are currently regarded as a major threat to biodiversity and agriculture all over the world, often resulting in huge economic losses. Apparent importance of this issue has brought to life various strategies of invasive species management. The concept of biological control is based on the assumption that the impact of certain biological or environmental factors can slow down or block the spread of harmful species. Several such factors have been identified earlier. In this talk, we consider how the rate of invasion and the whole pattern of spread can possibly be affected by the impact of predation.

We consider a model of the invasive insect spread controlled by its specialist predator. Mathematically, the system is described by two nonlinear partial differential equations of diffusion-reaction type. We first try to treat the problem analytically. Under some additional constraints, we obtain its exact solution. Having considered the solution properties, we show that predation can indeed block or even reverse the invasive species spread provided the population growth is damped by the strong Allee effect. We then study the problem by means of extensive numerical experiments in one and two spatial dimensions and show that the impact of predation can change the whole pattern of spread. In a certain parameter range, invasion can take place not via the intuitively expected circular expanding population front but via motion and interaction of separate patches. The population density appears to be on the order of carrying capacity inside the patches and it is virtually zero between the patches. Remarkably, a similar pattern of spread can be seen in data field observations. We then show that this phenomenon of patchy invasion takes place "at the edge of extinction."

A counter-intuitive finding following from our results is that the invasion success depends on the magnitude of the controlling effort in a non-monotonous way. An increase in control may reinstate the invasion that would fail otherwise. A message to pest control managers is therefore that a better result may sometimes be achieved by investing less money, contrary to what is usually done.

Jon Pitchford, University of York "Marine reserves and uncertain trade-offs"

Economic and environmental processes are, by their very nature, unpredictable. Mathematical models need to respect this fact, and to incorporate such uncertainties in a rigorous manner. Simply computing the expected outcome of a policy can be very misleading in both the long- and short terms. In this presentation I illustrate these ideas with reference to the sustainable management of exploited fish stocks. The implementation of marine reserves (no-take zones) typically causes a decrease in expected yield, but this expected value is meaningless in the context of sustainable management; the corresponding decreases in interannual variability and probability of stock collapse provide strong motivation for reserve implementation. These conclusions are drawn from a highly idealised model. By adding complexity, in particular by assessing the roles of migratory behaviour and evolution in movement and life history, the story becomes more complicated but the essential message is unchanged; reserves can be an effective management tool provided they are implemented at appropriate spatial and temporal scales, and provided the criteria for assessing their effectiveness are more sophisticated than a simple expected value.

Mark Preston, University of York
“When to be mean?”

In this talk I will present two models for fish stock recruitment and, more importantly, how to better analyse stochastic data rather than recourse to mean field analysis. Reference will be made to actuarial mathematics, epidemiology, genetic algorithms, continuous time Markov chains, game theory as well as fish.

Frank Riedel , University of Bielefeld
“Irreversible Investment Problems under Ambiguity”

In economics, the probability distributions of returns is frequently not well known. This is particularly true for situations when a firm invests into a new project or technology where few data are available. In this situation, we speak of model uncertainty or Knightian ambiguity.

We present an overview of recent results in real options theory under Knightian uncertainty. A general theory for optimal stopping problems under multiple priors is developed. Subsequently, we apply this theory to some specific problems like the standard entry problem (call option); we also look at more complex examples like exotic options of the Barrier or Shout type.

Yacov Tsur, The Hebrew University of Jerusalem
“Resource management in a fragile environment”

Exploitation diminishes the capacity of renewable resources to withstand environmental stress, increasing their vulnerability to extreme conditions that may trigger abrupt changes. The onset of such events depends on the coincidence of extreme environmental conditions (environmental threat) and the resource state (determining its resilience). When the former is uncertain and the latter evolves stochastically, the uncertainty regarding the event occurrence is the result of the combined effect of these two uncertain components. The environmental threat renders the single-period discount factor policy-dependent and, as a result, the compound discount factor becomes history-dependent. We study optimal management in such a setting. Existence of an optimal Markovian-deterministic stationary policy is established and long run properties are characterized. A numerical example illustrates these properties.