Narrow Results

The purpose of this paper is to develop an explicit construction of consistent utilities, using the stochastic flows approach developed in El Karoui & Mrad (2013, 2020). Starting from a family of utility functions indexed by some parameter $\alpha$ (for example, the risk aversion coefficient or any other parameter), the idea is to randomize $\alpha$ and to construct nonstandard stochastic utility processes. Two approaches are developed. The first one consists of building directly from the class $\{U^{\alpha },\alpha \in ℝ\}$ a global utility $U$ as a sup-convolution. The second approach which is very different, consists to define from the class ${(X^{\alpha },Y^{\alpha })}_{\alpha \in ℝ}$ of monotonic optimal processes, associated with the class $\{U^{\alpha },\alpha \in ℝ\}$, a global pair $(X^{\ast },Y^{\ast })$ as a mixture. The nonstandard stochastic utility is then obtained by composing stochastic flows and is interpreted as the aggregate utility of all considered agents.

In this work, we study a class of consistent dynamic utilities in a incomplete financial market including jumps. First, we show that the dynamic utility is solution of a non-linear second-order stochastic partial integro-differential equation (SPIDE). Second, a complete study of the primal and the dual problems, allows us, firstly, to establish a connection between the utility-SPIDE and two SDEs satisfied by the optimal processes. Based on this connection, stochastic flow technics for SDEs and characteristic method, the SPIDE is completely solved and monotony and concavity properties of the solution are proved.

Current interpretations of strategic environmental assessment (SEA) revolve around two main ideas. Firstly, SEA is seen as a concept for improving decision making through the assessment of environmental and potentially other impacts, not following any prescribed form, thus being flexible and leaving ample space for different interpretation. Secondly, a more rational view is taken and SEA is regarded a systematic instrument for improving decision making through assessment of the environmental and potentially other impacts, following a prescribed set of procedural stages and possibly other methodological aspects. Adopting the argument of the latter idea, this paper suggests that SEA performance criteria are not equally valid for every SEA, but differ for three distinct SEA types; policy-SEA, plan-SEA and programme-SEA. In order to provide empirical evidence, 25 assessments for transport and spatial/land use policies, plans and programmes (PPPs) are evaluated, based on the performance criteria introduced by the International Association for Impact Assessment (IAIA) at the Glasgow meeting in 1999 and endorsed in November 2001.