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Optimization of conditional convex risk measure is a central theme in dynamic portfolio selection theory, which has not yet systematically studied in the previous literature perhaps since conditional convex risk measures are neither random…

Optimization and Control · Mathematics 2019-10-24 Tiexin Guo

In this paper, we prove that under the domination condition: \begin{equation*} {\cal{E}}^{-\mu,-\nu}[-\xi|{\cal{F}}_t]\leq\rho_t(\xi)\leq{\cal{E}}^{\mu,\nu}[-\xi|{\cal{F}}_t],\quad \forall\xi\in \mathcal{L}^{\exp}_T\ (\text{resp.}\…

Probability · Mathematics 2026-03-20 Shiqiu Zheng

The inf-convolution of risk measures is directly related to risk sharing and general equilibrium, and it has attracted considerable attention in mathematical finance and insurance problems. However, the theory is restricted to finite sets…

Risk Management · Quantitative Finance 2022-03-22 Marcelo Brutti Righi , Marlon Ruoso Moresco

We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and…

Portfolio Management · Quantitative Finance 2012-12-18 Sara Biagini , Jocelyne Bion-Nadal

We define and develop an approach for risk budgeting allocation - a risk diversification portfolio strategy - where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions…

Mathematical Finance · Quantitative Finance 2024-11-01 Silvana M. Pesenti , Sebastian Jaimungal , Yuri F. Saporito , Rodrigo S. Targino

This paper introduces and fully characterizes the novel class of quasi-logconvex measures of risk, to stand on equal footing with the rich class of quasi-convex measures of risk. Quasi-logconvex risk measures naturally generalize logconvex…

Risk Management · Quantitative Finance 2022-08-17 Roger J. A. Laeven , Emanuela Rosazza Gianin

We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a c\`adl\`ag nonlinear…

Risk Management · Quantitative Finance 2013-06-18 Marcel Nutz , H. Mete Soner

In this paper, we investigate risk minimization problem of derivatives based on non-tradable underlyings by means of dynamic g-expectations which are slight different from conditional g-expectations. In this framework, inspired by [1] and…

Portfolio Management · Quantitative Finance 2012-08-13 Tianxiao Wang

This survey gives an introduction to monetary measures of risk as monotone and cash additive functions on spaces of univariate random variables. Primal and dual representation results as well as several examples are discussed. Principal…

Risk Management · Quantitative Finance 2018-12-12 Andreas H Hamel

Monetary risk measures are usually interpreted as the smallest amount of external capital that must be added to a financial position to make it acceptable. We propose a new concept: intrinsic risk measures and argue that this approach…

Risk Management · Quantitative Finance 2016-10-28 W. Farkas , A. Smirnow

This paper investigates risk measures derived from the expected maximum deficit in a continuous-time framework and develops optimal reserve allocation strategies across multiple lines of business. We formalize the expected maximum deficit…

Risk Management · Quantitative Finance 2026-05-19 Claude Lefevre , Pierre Zuyderhoff

We address the problem that classical risk measures may not detect the tail risk adequately. This can occur for instance due to averaging when calculating the Expected Shortfall. The current literature proposes the so-called adjusted…

Mathematical Finance · Quantitative Finance 2025-04-24 Jascha Alexander , Christian Laudagé , Jörn Sass

In this paper we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency we require that a dynamic deviation measures satisfies a…

Probability · Mathematics 2016-04-28 Martijn Pistorius , Mitja Stadje

The aim of this work is to study risk measures generated by distortion functions in a dynamic discrete time setup, and to investigate the corresponding dynamic coherent acceptability indices (DCAIs) generated by families of such risk…

Risk Management · Quantitative Finance 2023-09-11 Tomasz R. Bielecki , Igor Cialenco , Hao Liu

We propose a new class of mappings, called Dynamic Limit Growth Indices, that are designed to measure the long-run performance of a financial portfolio in discrete time setup. We study various important properties for this new class of…

Risk Management · Quantitative Finance 2014-07-22 Tomasz R. Bielecki , Igor Cialenco , Marcin Pitera

In this paper we will provide a representation of the penalty term of general dynamic concave utilities (hence of dynamic convex risk measures) by applying the theory of g-expectations.

Probability · Mathematics 2009-12-16 Freddy Delbaen , Shige Peng , Emanuela Rosazza Gianin

The financial crisis has dramatically demonstrated that the traditional approach to apply univariate monetary risk measures to single institutions does not capture sufficiently the perilous systemic risk that is generated by the…

Mathematical Finance · Quantitative Finance 2015-04-27 Francesca Biagini , Jean-Pierre Fouque , Marco Frittelli , Thilo Meyer-Brandis

The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be…

Risk Management · Quantitative Finance 2014-05-22 Zachary Feinstein , Birgit Rudloff

Recently, literature on dynamic coherent risk measures has broadened the choices for risk-sensitive performance evaluation. A running example includes Cumulative prospect theory and Conditional variance at risk. Most of them can be can be…

Optimization and Control · Mathematics 2020-12-14 Weixin Wang

The family of admissible positions in a transaction costs model is a random closed set, which is convex in case of proportional transaction costs. However, the convexity fails, e.g. in case of fixed transaction costs or when only a finite…

Risk Management · Quantitative Finance 2021-01-15 Andreas Haier , Ilya Molchanov