Dynamically consistent Choquet random walk and real investments

In the real investments literature, the investigated cash flow is assumed to follow some known stochastic process (e.g. Brownian motion) and the criterion to decide between investments is the discounted utility of their cash flows. However, for most new investments the investor may be ambiguous about the representation of uncertainty. In order to take such ambiguity into account, we refer to a discounted Choquet expected utility in our model. In such a setting some problems are to dealt with: dynamical consistency, here it is obtained in a recursive model by a weakened version of the axiom. Mimicking the Brownian motion as the limit of a random walk for the investment payoff process, we describe the latter as a binomial tree with capacities instead of exact probabilities on its branches and show what are its properties at the limit. We show that most results in the real investments literature are tractable in this enlarged setting but leave more room to ambiguity as both the mean and the variance of the underlying stochastic process are modified in our ambiguous model.

Valuing future cash flows with non separable discount factors and non additive subjective measures: Conditional Choquet Capacities on Time and on Uncertainty

We consider future cash flows that are contingent both on dates in time and on uncertain states. The decision maker (DM) values the cash flows according to its decision criterion: Here the payoffs’ expectation with respect to a capacity measure. The subjective measure grasps the DM’s behaviour in front of the future, in the spirit of de Finetti’s (1930) and of Yaari’s (1987) Dual Theory in the case of risk. Decomposition of the criterion into two criteria that represent the DM’s preferences on uncertain payoffs and time contingent payoffs are derived from Ghirardato’s (1997) results. Conditional Choquet integrals are defined by dynamic consistency requirements and conditional capacities are derived, under some conditions on information. In contrast with other models referring to dynamic consistency, ours doesn’t collapse into a linear one because it violates a weak version of consequentialism.

Dynamically consistent Choquet random walk and real investments

In the real investments literature, the investigated cash flow is assumed to follow some known stochastic process (e.g. Brownian motion) and the criterion to decide between investments is the discounted utility of their cash flows. However, for most new investments the investor may be ambiguous about the representation of uncertainty. In order to take such ambiguity into account, we refer to a discounted Choquet expected utility in our model. In such a setting some problems are to dealt with: dynamical consistency, here it is obtained in a recursive model by a weakened version of the axiom. Mimicking the Brownian motion as the limit of a random walk for the investment payoff process, we describe the latter as a binomial tree with capacities instead of exact probabilities on its branches and show what are its properties at the limit.  We show that most results in the real investments literature are tractable in this enlarged setting but leave more room to ambiguity as both the mean and the variance of the underlying stochastic process are modified in our ambiguous modelChoquet integrals; conditional Choquet integrals; random walk; Brownian motion; real options; optimal portfolio

CONSISTENT DYNAMICE CHOICE AND NON-EXPECTED UTILITY PREFERENCES

Pursuing works from Sarin and Wakker (1998), we study how NonExpected Utility models could be consistently applied to multi-stage decision problems. Concerning multiple priors model, we remove the argument that dynamic consistency, consequentialism and model consistency (sequential consistency in Sarin and Wakker (1998)) can all be preserved. Like Choquet expected utility, deviation of expected utility is only allowed over the final stage. Moreover, it's proved for the two models that if we also assume reduction of compound acts, then an expected utility representation exists in all stages.Choquet Expected Utility, Multiple Priors, Sequential Choice, Dynamic Consistency, Consequentialism, Reduction of Compound Acts.

Employee ownership as a signal of management quality

The employees' decision to become shareholder of the company they work for can be a consequence of employers' matching contribution in company stock. From a behavioral perspective, employees would regard these contributions as an implicit investment advice made by their employer. This paper adopts another viewpoint. Since employee ownership can be used as an entrenchment mechanism, we suggest that employer's matching policy can be considered as an imperfect signal of management quality. This paper suggests that employee ownership can be used by managers to compensate their management skills to the market. It recommends that employee ownership policy should not be influenced by the managers.Employee ownership ; corporate governance ; management entrenchment

Attitude toward information and learning under multiple priors

This paper studies learning under multiple priors by characterizing the decision maker's attitude toward information. She is incredulous if she integrates new information with respect to only those measures that minimizes the likelihood of the new information and credulous if she uses the maximum likelihood procedure to update her priors. Both updating rules expose her to dynamic inconsistency. We explore different ways to resolve this problem. One way consists to assume that the decision maker's attitude toward information is not relevant to characterize conditional preferences. In this case, we show that a necessary and sufficient condition, introduced by [Epstein L. and Schneider M., 2003. Recursive multiple priors. Journal of Economic Theory 113, 1-31], is the rectangularity of the set of priors. Another way is to extend optimism or pessimism to a dynamic set-up. A pessimistic (max-min expected utility) decision maker will be credulous when learning bad news but incredulous when learning good news.Conversely, an optimistic (max-max expected utility) decision maker will be credulous when learning good news but incredulous when learning bad news. It allows max-min (or max-max) expected utility preferences to be dynamically consistent but it violates consequentialism because conditioning works with respect to counterfactual outcomes. The implications of our findings when the set of priors is the core of a non-additive measure are explored.Multiple priors ; Learning ; Dynamic consistency ; Consequentialism ; Attitude toward information

Real Options under Choquet-Brownian Ambiguitys

Real options models characterized by the presence of “ambiguity” (or “Knightian uncertainty”) have been recently proposed. But based on recursive multiple-priors preferences, they typically describe ambiguity through a range of Geometric Brownian motions and solve it by application of a maxmin expected utility criterion among them (worst case). This reduces acceptable individual preferences to the single case of an extreme form of pessimism. In contrast, by relying on dynamically consistent “Choquet-Brownian” motions to represent the ambiguous cash flows expected from a project, we show that a much broader spectrum of attitudes towards ambiguity may be accounted for, improving the explanatory and application potentials of these appealing expanded real options models. In the case of a perpetual real option to invest, ambiguity aversion may delay the moment of exercise of the option, while the opposite holds true for an ambiguity seeking decision maker. Furthermore, an intricate relationship between risk and ambiguity appears strikingly in our model.