Value at risk (VaR) is the standard measure of market risk used by financial institutions. Interpreting the VaR as the quantile of future portfolio values conditional on current information, the conditional autoregressive value at risk (CAViaR) model specifies the evolution of the quantile over time using an autoregressive process and estimates the parameters with regression quantiles. Utilizin...

The classical risk-neutral newsvendor problem is to decide the order quantity to maximize the one period expected pro.t under a given demand distribution. In this paper we consider a risk-averse newsvendor with a stochastic price-dependent demand. We use the Conditional Value-at-Risk (CVaR), a risk measure commonly used in finance, as the decision criterion. The aim of our study is to investiga...

The aim of the paper is to propose a preferences representation under risk where risk perception can be past experience dependent. A first step consists in considering a one period decision problem where individual preferences are no more defined only on decisions but on pairs (decision, past experience). The obtained criterion is used in the construction of a dynamic choice model under risk. T...

We propose a new class of mappings, called Dynamic Limit Growth Indices, that are designed to measure the long-run performance of a nancial portfolio in discrete time setup. We study various important properties for this new class of measures, and in particular, we provide necessary and su cient condition for a Dynamic Limit Growth Index to be a dynamic assessment index. We also establish their...

Johnstone and Silverman (1997) described a level-dependent thresholding method for extracting signals from correlated noise. The thresholds were chosen to minimize a data based unbiased risk criterion. Here we show that in certain asymptotic models encompassing short and long range dependence, these methods are simultaneously asymptotically minimax up to constants over a broad range of Besov cl...

An agent has Hurwicz criterion with pessimismoptimism index α under imprecise risk and adopts the root dictatorship version of McClennen’s Resolute Choice in sequential decision situations, i.e. evaluates strategies at the root of the decision tree by the Hurwicz criterion and enforces the best strategy, thus behaving in a dynamically consistent manner. We address two questions raised by this t...

The presence of options in a portfolio fundamentally alters the portfolio’s risk and return profiles when compared to an all equity portfolio. In this paper, we advocate modeling a risk-based criterion for optioned portfolio selection and rebalancing problems. The criterion is inspired by Chicago Mercantile Exchange’s risk-based margining system which sets the collateralization requirements on ...

We study a risk-averse newsvendor problem with quantity competition and price competition. Under the Conditional Value-at-Risk (CVaR) criterion, we characterize the optimal quantity and pricing decisions under both quantity and price competition. For quantity competition, we consider two demand splitting rules, namely proportional demand allocation and demand reallocation. Although competition ...

In decision-making under uncertainty there are two main questions that need to be evaluated: (i) What are the future consequences and associated uncertainties of an action, and (ii) what is a good (or right) decision or action. Philosophically these issues are categorized as epistemic questions (i.e. questions of knowledge) and ethical questions (i.e. questions of moral and norms). This paper d...

Credit migration or transition matrices, which characterize the expected changes in credit quality of obligors, are cardinal inputs to applications such as asset pricing and risk management. We propose a new metric for comparing these matrices (a mobility index) by first subtracting the identity matrix, focusing the analysis on the dynamics, and then taking the average of the singular values fo...