Related papers: Multiportfolio time consistency for set-valued con…
Monitoring means to observe a system for any changes which may occur over time, using a monitor or measuring device of some sort. In this paper we formulate a problem of monitoring dates of maximal risk of a financial position. Thus, the…
This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time…
One of the crucial problems in mathematical finance is to mitigate the risk of a financial position by setting up hedging positions of eligible financial securities. This leads to focusing on set-valued maps associating to any financial…
This paper deals with multidimensional dynamic risk measures induced by conditional $g$-expectations. A notion of multidimensional $g$-expectation is proposed to provide a multidimensional version of nonlinear expectations. By a technical…
In this paper we provide a flexible framework allowing for a unified study of time consistency of risk measures and performance measures (also known as acceptability indices). The proposed framework not only integrates existing forms of…
This paper characterizes the equilibrium in a continuous time financial market populated by heterogeneous agents who differ in their rate of relative risk aversion and face convex portfolio constraints. The model is studied in an…
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…
We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the…
We provide analytical results for a static portfolio optimization problem with two coherent risk measures. The use of two risk measures is motivated by joint decision-making for portfolio selection where the risk perception of the portfolio…
Choosing a portfolio of risky assets over time that maximizes the expected return at the same time as it minimizes portfolio risk is a classical problem in Mathematical Finance and is referred to as the dynamic Markowitz problem (when the…
In this work we study the Lebesgue property for convex risk measures on the space of bounded c\`adl\`ag random processes ($\mathcal{R}^\infty$). Lebesgue property has been defined for one period convex risk measures in \cite{Jo} and earlier…
We consider portfolio selection when decisions based on a dynamic risk measure are affected by the use of a moving horizon, and the possible inconsistencies that this creates. By giving a formal treatment of time consistency which is…
When we implement a portfolio selection methodology under a mean-risk formulation, it is essential to correctly model investors' risk aversion which may be time-dependent, or even state-dependent during the investment procedure. In this…
Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are…
In this paper we present a framework for risk-averse model predictive control (MPC) of linear systems affected by multiplicative uncertainty. Our key innovation is to consider time-consistent, dynamic risk metrics as objective functions to…
Two approaches to time consistency of risk averse multistage stochastic problems were discussed in the recent literature. In one approach certain properties of the cor-responding risk measure are postulated which imply its decomposability.…
We employ model predictive control for a multi-period portfolio optimization problem. In addition to the mean-variance objective, we construct a portfolio whose allocation is given by model predictive control with a risk-parity objective,…
In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel…
We propose a new procedure for the risk measurement of large portfolios. It employs the following objects as the building blocks: - coherent risk measures introduced by Artzner, Delbaen, Eber, and Heath; - factor risk measures introduced in…
This paper focuses on a dynamic multi-asset mean-variance portfolio selection problem under model uncertainty. We develop a continuous time framework for taking into account ambiguity aversion about both expected return rates and…