Financial market equilibria with cumulative prospect theory

The paper first shows that financial market equilibria need not to exist if agents possess cumulative prospect theory preferences with piecewise-power value functions. This is due to the boundary behavior of the cumulative prospect theory value function, which might cause an infinite short-selling problem. But even when a non-negativity constraint on final wealth is added, non-existence can occur due to the non-convexity of CPT preferences, which might cause discontinuities in the agents’ demand functions. This latter observation also implies that concavification arguments which has been used in portfolio allocation problems with CPT preferences do not apply to our general equilibrium setting with finite many agents. Existence of equilibria is established when non-negativity constraints on final wealth are imposed and there is a continuum of agents in the market. However, if the original prospect theory is used instead of cumulative prospect theory, then other discontinuity problems can cause non-existence of market equilibria even in this case.     

Inter-temporal preference for flexibility and risky choice

We derive an inter-temporal theory of choice, in the spirit of Kreps and Porteus [Kreps, D.M., Porteus, E.L., 1978. Temporal resolution of uncertainty and dynamic choice theory. Econometrica 46, 185–200], where decision makers have incomplete preferences. This can be used to model indecisiveness as well as unforeseen contingencies. The key to our approach is a time consistency condition and therefore the normative connection between ex-ante and ex-post choice. The time consistency condition enables a representation that is a straight forward extension of recursive utility with the exception that it features an inter-temporal ‘utility for flexibility’.     

Agricultural arbitrage and risk preferences

A structural intertemporal model of agricultural asset arbitrage equilibrium is developed and applied to agriculture in the North Central region of the US. The data are consistent with a unifying level of risk aversion. The levels of risk aversion are more plausible than previous estimates for agriculture. However, the standard arbitrage equilibrium is rejected; perhaps, this is due to the period and the shortness of the period studied.     

Nonparametric Bayesian modelling of monotone preferences for discrete choice experiments

Discrete choice experiments are widely used to learn about the distribution of individual preferences for product attributes. Such experiments are often designed and conducted deliberately for the purpose of designing new products. There is a long-standing literature on nonparametric and Bayesian modelling of preferences for the study of consumer choice when there is a market for each product, but this work does not apply when such markets fail to exist as is the case with most product attributes. This paper takes up the common case in which attributes can be quantified and preferences over these attributes are monotone. It shows that monotonicity is the only shape constraint appropriate for a utility function in these circumstances. The paper models components of utility using a Dirichlet prior distribution and demonstrates that all monotone nondecreasing utility functions are supported by the prior. It develops a Markov chain Monte Carlo algorithm for posterior simulation that is reliable and practical given the number of attributes, choices and sample sizes characteristic of discrete choice experiments. The paper uses the algorithm to demonstrate the flexibility of the model in capturing heterogeneous preferences and applies it to a discrete choice experiment that elicits preferences for different auto insurance policies.     

Revealed preferences: A topological approach

The purpose of this paper is to study the relationship between the axiomatic foundations of revealed preference theory and the continuity properties of choice. The main result of this paper shows that the continuity of a set-to-point choice function is equivalent to the weak axiom of revealed preference and openness of the strict revealed relation, provided that the collection of budget sets is endowed with a topology used widely by economists.     

Revealed preference theory on the choice of lotteries

The choice behavior of a decision-maker is said to be consistent with expected utility maximization if there exists a utility function defined on the set of prizes such that the decision-maker chooses lotteries with the highest expected utility. We present a revealed preference characterization of choice behavior that is consistent with expected utility maximization. A necessary and sufficient condition for expected utility maximization is that there does not exist a way to compound lotteries such that the probability distribution over the final prizes generated by the chosen lotteries of each observation is equal to that generated by the rejected lotteries of each observation. Our result is quite general and can be applied to any compact set of prizes and any choice correspondence.     

Demand properties of concavifiable preferences

The purpose of the present paper is to clarify the relation between choice theory for individual consumers, i.e., the observed demand behavior, and the preference ordering ?$?$ of that individual. Specifically, we study how concavifiability (i.e., representability of ?$?$ by a concave utility function) is expressed by quantities (cross-coefficients) appearing in revealed preferences theory. We present a sequence of rather explicit necessary conditions for concavifiability. All these conditions are quantitative asymptotic strengthenings of the strong axiom of revealed preference. The results and concepts are illustrated by means of examples in which an expenditure data is defined by providing its generating utility function.     

Strictly monotonic preferences on continuum of goods commodity spaces

We consider a set K of differentiated commodities. A preference relation on the set of consumption plans is strictly monotonic whenever to consume more of at least one commodity is more preferred. It is an easy task to find examples of strictly monotonic preference relations when K   is finite or countable. However, it is not easy for spaces like ?^∞([0,1])${?}^{\infty }([0\text{,}1])$, the space of bounded functions on the unit interval.     

Separability of stochastic production decisions from producer risk preferences in the presence of financial markets

Separation results, as they are usually understood, refer to conditions under which a firm’s production decisions are independent of its risk attitudes. Well-understood situations where separation occurs typically include those where technically feasible production opportunities are replicable in financial markets. This paper gives necessary and sufficient conditions for separation that go beyond these well-understood spanning conditions. To do so, we present a unified treatment of the production and financial decisions available to a firm facing frictionless financial markets and a stochastic production technology under minimal assumptions about the firm’s technology and objective function.     

Informational cascades with endogenous prices: The role of risk aversion

In this paper, we show that long run market informational inefficiency and informational cascades can easily happen when trades occur at market clearing prices. We consider a sequential trade model where: (i) the investors’ set of actions is discrete; (ii) dealers and investors differ in risk aversion; (iii) investors’ information is bounded. We show that informational cascade occurs as soon as traders’ beliefs do not differ too sharply. Thus, prices cannot fully incorporate the private information dispersed in the economy.     

Quantification of preferences in markets

In this paper we quantify agent preferences in a market. In our framework every agent has a utility level associated with each transaction, and we assume that the probability of a feasible market transaction increases with an increase in total utility. It is surprising to observe that this simple behavioral principle induces a usually unique probability measure that can be constructed by a fast numerical algorithm. This unusual combination of a rigorous model and a fast numerical algorithm makes it possible to construct a well-defined set of preferences that implies a set of observed commodity prices.     

Global identification of risk preferences with revealed preference data

The concept of parameter identification (for a given specification) is differentiated from global identification (which specification is right). First-order conditions for production under risk are shown to admit many alternative specification pairs representing risk preferences and either perceived price risk, production risk, or the deterministic production structure. Imposing an arbitrary specification on any of the latter three determines which risk preference specification fits a given dataset, undermining global identification even when parameter identification is suggested by typical statistics. This lack of identification is not relaxed by increasing the number of observations. Critical implications for estimation of mean-variance specifications are derived.     

Nonparametric estimation of conditional VaR and expected shortfall

This paper considers a new nonparametric estimation of conditional value-at-risk and expected shortfall functions. Conditional value-at-risk is estimated by inverting the weighted double kernel local linear estimate of the conditional distribution function. The nonparametric estimator of conditional expected shortfall is constructed by a plugging-in method. Both the asymptotic normality and consistency of the proposed nonparametric estimators are established at both boundary and interior points for time series data. We show that the weighted double kernel local linear conditional distribution estimator has the advantages of always being a distribution, continuous, and differentiable, besides the good properties from both the double kernel local linear and weighted Nadaraya–Watson estimators. Moreover, an ad hoc data-driven fashion bandwidth selection method is proposed, based on the nonparametric version of the Akaike information criterion. Finally, an empirical study is carried out to illustrate the finite sample performance of the proposed estimators.     

Exit problems in regime-switching models

This paper provides a general framework for pricing of perpetual American and real options in regime-switching Lévy models. In each state of the Markov chain, which determines switches from one Lévy process to another, the payoff stream is a monotone function of the Lévy process labeled by the state. This allows for additional switching within each state of the Markov chain (payoffs can be different in different regions of the real line). The pricing procedure is efficient even if the number of states is large provided the transition rates are not very large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modeled as finite-state Markov chains. As an application, we solve exit problems for a price-taking firm, and study the dependence of the exit threshold on the interest rate uncertainty.     

Optimal stopping made easy

This paper presents a simple discrete time model for valuing real options. A short and simple proof of optimal exercise rules for the standard problems in the real options theory is given in the binomial and trinomial models, and, more generally, when the underlying uncertainty is modelled as a random walk on a lattice. The method of the paper is based on the use of the expected present value operators. With straightforward modifications, the method works in discrete time-continuous space, continuous time-continuous space and continuous time-discrete space models.