In this paper we consider the notion of rectangularity of a set of probability measures, introduced in Epstein and Schneider (2003), from a somewhat different point of view. We define rectangularity as a property of dynamic decomposition of a distributionally robust stochastic optimization problem and show how it relates to the modern theory of coherent … Read more
Coherent risk measures have become a popular tool for incorporating risk aversion into stochastic optimization models. For dynamic models in which un-certainly is resolved at more than one stage, however, use of coherent risk measures within a standard single-level optimization framework presents the modeler with an uncomfortable choice between two desirable model properties, time consistency … Read more
We study the exploitation of a one species forest plantation when timber price is uncertain. The work focuses on providing optimality conditions for the optimal harvesting policy in terms of the parameters of the price process and the discount factor. We use risk averse stochastic dynamic programming and use the Conditional Value-at-Risk (CVaR) as our … Read more
In this paper we discuss time consistency of risk averse multistage stochastic programming problems. We show, in a framework of finite scenario trees, that composition of law invariant coherent risk measures can be law invariant only for the expectation or max-risk measures. CitationPreprintArticleDownload View PDF
In this paper we discuss representations of law invariant coherent risk measures in a form of integrals of the Average Value-at-Risk measures. We show that such integral representation exists iff the dual set of the considered risk measure is generated by one of its elements, and this representation is uniquely defined. On the other hand, … Read more
In this paper we study relations between the minimax, risk averse and nested formulations of multistage stochastic programming problems. In particular, we discuss conditions for time consistency of such formulations of stochastic problems. We also describe a connection between law invariant coherent risk measures and the corresponding sets of probability measures in their dual representation. … Read more
In this paper we consider the adjustable robust approach to multistage optimization, for which we derive dynamic programming equations. We also discuss this from a point of view of risk averse stochastic programming. As an example we consider a robust formulation of the classical inventory model and show that, similar to the risk neutral case, … Read more
In this paper we discuss time consistency of multi-stage risk averse stochastic programming problems. We approach the concept of time consistency from an optimization point of view. That is, at each state of the system optimality of a decision policy should not involve states which cannot happen in the future. We also discuss a relation … Read more
In this work we introduce a class of measures for evaluating the quality of financial positions based on their ability to achieve desired financial goals. In the spirit of Simon (1959), we call these measures satisficing measures and show that they are dual to classes of risk measures. This approach has the advantage that aspiration … Read more
In this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems. We argue that two stage (say linear) stochastic programming problems can be solved with a reasonable accuracy by Monte Carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the … Read more