Uncertain Payoffs Research Articles

Essays on Uncertainty and Decision-Making in Environmental Economics

This draft PhD thesis analyzes four issues in the research field that consists of the intersection of environmental economics, uncertainty, and decision-making. 1. Economic investments that lead to environmental damages beyond repair - like cutting rainforests or emitting pollutants with long life times - can be interpreted as irreversible investments with uncertain pay-offs. In the context of irreversible investments under uncertainty two different concepts of option value were developed. They account for the value of keeping options open - i.e. postponing the irreversible investment - in the presence of potential future learning about the social profitability of the investment. These are the concept of quasi-option value (value of information) developed in the environmental and resource economic literature and the concept of real option value (value of the option to postpone) developed in the financial economics literature. This thesis shows that the quasi-option value (value of information) is that part of the real option value (value of the option to postpone) that is related to uncertainty being resolved over time. This means that common knowledge in the environmental and resource economic literature with respect to the relation of both concepts is not correct. 2. If marginal damages of pollution rise with the pollution level, low marginal pollution abatement costs demand a relatively low Pigouvian tax - the pollution tax level that leads to optimal abatement. As a result, to determine the Pigouvian tax level, a regulator needs to know pollution abatement costs, information that is privately owned by individual pollutors. Unfortunately, pollutors have no intention to reveal their true abatement costs. One text book solution to this problem is that the regulator keeps adapting the tax level until the pollution tax leads to an emission level resulting in marginal damages equal to the tax level - the criterium for social optimality. That is, only after an unspecified amount of time and abatement adaptation costs the socially optimal abatement level is reached. This thesis shows there exists a non-linear tax system, the so called differential tax that triggers firms to reveal their abatement costs truthfully and will lead to socially optimal abatement levels instantly, thereby reducing social costs compared to the iterative solution. 3. In the presence of environmental innovation, future abatement costs are unknown by the polluting firms as well. Under those circumstances the regulator is needs a tax system that is flexible with respect to falling abatement costs through innovation (please recall that lower marginal abatement costs demand a lower Pigouvian tax) as well as keeps incentives for innovation - created by pollution taxes after innovation - upright. This thesis analyzes the effects of a robust second-best pollution taxation scheme that combines flexibility to cope with changing marginal abatement costs with commitment to relatively high tax levels to create incentives for environmental innovation. It shows that this instrument is superior to time consistent taxation. Superiority of the flexible taxation scheme with respect to commitment to a linear tax could not be shown. 4. The use of quantitative model results to support policy making is one way social sciences might have a positive effect on real world decision making. This thesis identifies decision-maker related potential errors made in the interpretation of quantitative model results. It is argued these errors can be prevented by the social scientist by stating explicitly for which policy maker and for what purpose the model results are meant for.

Attribution of Deaths Following Cancer Treatment

Attribution of Deaths Following Cancer Treatment

Hedging in Incomplete Markets: An Approximation Procedure for Practical Application

AbstractDerivative financial instruments are frequently used as a tool for influencing the risk of entrepreneurial uncertain payoff. To this end, an approximation procedure is developed capable of calculating the optimal quantity of derivatives to be used. It is assumed that the entrepreneurial cash flow is governed by several stochastic factors and that derivatives are only available as a hedging tool for one of these factors. In general, it is easy to determine optimal hedging payment structures with respect to this factor, but real‐life hedging opportunities will typically not allow to perfectly reproduce such a fictitious payment structure, thus leading to complex numerical optimization problems. Instead of directly approximating the entrepreneurial expected utility maximum, we suggest using the fictitious optimal hedging payment structure as a starting point and to minimize the quadratic deviation between payment structures realizable by financial derivatives actually available and the resulting entrepreneurial payoff achieving the fictitious optimal hedging payment structure. This approach proves to be rather easy. Indeed, under certain conditions an explicit solution can be reached. After analyzing the qualitative properties of our approximation solution, we examine its efficiency for two practical hedging problems. In the first example, we get nearly the same solutions with our approximation procedure as with a grid programming approach presented by some other authors. Among other things, our second example may explain why some special kinds of financial derivatives, known as shared currency option under tenders, are not used in international invitations for tenders even though they offer hedging opportunities that are otherwise not available. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21: 599–631, 2001

Dynamic Games with Uncertain Payoffs

Cooperative differential games with uncertain payoffs are considered. The new solution concepts based on Shapley value are introduced and their realizability, strong realizability, time consistency and internal consistency are proved.

Why Imitate, and If So, How?: A Boundedly Rational Approach to Multi-armed Bandits

Individuals in a finite population repeatedly choose among actions yielding uncertain payoffs. Between choices, each individual observes the action and realized outcome ofoneother individual. We restrict our search to learning rules with limited memory that increase expected payoffs regardless of the distribution underlying their realizations. It is shown that the rule that outperforms all others is that which imitates the action of an observed individual (whose realized outcome is better than self) with a probability proportional to the difference in these realizations. When each individual uses this best rule, the aggregate population behavior is approximated by the replicator dynamic.Journal of Economic LiteratureClassification Numbers: C72, C79, D83.

The Valuation of Nonsystematic Risks and the Pricing of Swedish Lottery Bonds

Swedish government lottery bonds have coupon payments determined by lottery. They offer a unique opportunity to study a security with uncertain payoffs having a known, observable distribution. The risk associated with the lotteries is idiosyncratic by construction and should not command a risk premium in equilibrium. The bonds are traded in two forms, allowing us to evaluate the rewards to bearing extra lottery risk. Despite its idiosyncratic nature, we find prices appear to reflect aversion to this risk. We evaluate the empirical determinants of this differential pricing and possible explanations for it. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Joint Exploration and Investment in Exhaustible Resource Exploitation

The exploration and investment decisions for a resource producing firm are largely irreversible, not now-or-never propositions, and have uncertain future payoffs. As such, we show that, for such decisions to proceed, the expected discounted future returns to these decisions must outweigh the associated total direct user costs plus their respective option values. We then analyse the changes in the firm value should it engage in any of the above decisions. The model solution will also give the activating thresholds or the optimal decision rule for choosing between decisions. Lastly we specify parameter values for the model and put the optimal decision rule into practice.

An experiment on Coasian bargaining over ex ante lotteries and ex post rewards

We examine Coasian bargaining under uncertain payoff streams. Subjects bargained over both an ex ante lottery and the ex post reward. The results indicate nearly 87 percent of all agreements were Pareto efficient. However, only 7.3 percent were mutually advantageous, while nearly 85 percent of all agreements split the reward equally. Consequently, we remain cautious about policy recommendations based on the Coase theorem where uncertain payoffs exist. Finally, we find no evidence supporting the proposition that a fundamental difference exists between bargaining behavior over the ex ante lottery and the ex post rewards of an uncertain event.

CORPORATE APPLICATIONS OF CONTINGENT CLAIMS ANALYSIS: A SELECTIVE PERSPECTIVE

The purpose of this paper is to present a review of selected applications of contingent claims analysis in corporate finance. Contingent claims analysis is an approach to valuing payoffs which are contingent on other uncertain payoffs. The essential logic of the different applications reviewed is that we can value these derivative payoffs by replicating them with assets, whose prices are known. This simple logic is capable of providing one with insights into the pricing of new types of financial assets (e.g. optional bonds) as well as providing new insights into the valuation of strategic corporate investments.

Risk Sharing and Group Decision Making

In a decision-making problem where a group will receive an uncertain payoff which must be divided among the members of the group, the ultimate payoff of interest is the vector of individual payoffs received by the members of the group. In this paper, preferences are quantified in terms of cardinal utility functions for such vectors of payoffs. These utility functions can represent preferences concerning “equitable” and “inequitable” vectors of payoffs as well as attitudes toward risk. The individual utility functions are aggregated to form a group utility function for the vector of payoffs, and this latter function is, in turn, used to generate a group utility function for the overall group payoff and a sharing rule for dividing the group payoff into individual payoffs. The resulting group decisions are Pareto optimal in utility space. Properties of the sharing rule and the group utility function are investigated for additive and multilinear group utility functions.

Prices of State-Contingent Claims Implicit in Option Prices

The time-state preference approach to general equilibrium in an economy as developed by Arrow (1964) and Debreu (1959) is one of the most general frameworks available for the theory of finance under uncertainty. Given the prices of primitive securities (a security that pays $1.00 contingent upon a given state of the world at a given date, and zero otherwise, is a primitive This paper implements the time-state preference model in a multiperiod economy, deriving the prices of primitive securities from the prices of call options on aggregate consumption. These prices permit an equilibrium valuation of assets with uncertain payoffs at many future dates. Furthermore, for any given portfolio, the price of a $1.00 claim received at a future date, if the portfolio's value is between two given levels at that time, is derived explicitly from a second partial derivative of its calloption pricing function. An intertemporal capital asset pricing model is derived for payoffs that are jointly lognormally distributed with aggregate consumption. It is shown that using the Black-Scholes equation for options on aggregate consumption implies that individuals' preferences aggregate to isoelastic utility.

The Use of Distribution Functions to Represent Utility Functions

This paper considers the decision maker whose evaluation and consequent choice of actions is accomplished through the use of the expected utility hypothesis. In cases where the utility function is increasing with upper and lower bounds then the utility function can be characterized by a distribution function, and we can take advantage of the various properties of such functions as well as existing results with respect to such functions. Using these properties and results we can determine the certainty equivalents as a function of the parameters of the distribution function (utility function) and the parameters of the probability distribution on the uncertain payoff. The following cases are considered: (1) Gaussian distribution function and Gaussian probability distribution, (2) Exponential distribution function and exponential distribution and (3) Exponential distribution function and Gaussian probability distribution.