arXiv research

The paper studies dynamic star-shaped risk measures and their representation.

The paper characterizes dynamic return and star-shaped risk measures via BSDEs.

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 consistency properties of dynamic risk measures in terms of acceptance sets, penalty …

Develops a new method for risk diversification using dynamic risk measures.

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 result on explicit expressions for the comparison theorem, uniqueness theorem and…

Study dynamic risk measures with distributional uncertainty using optimal transport.

Risk measures applied to dynamic Markov processes with varying risk aversion.

This paper approaches the definition and properties of dynamic convex risk measures through the notion of a family of concave valuation operators satisfying certain simple and credible axioms. Exploring these in the simplest context of a finite time set and finite sample space, we find natural risk-transfer and time-co…

Enhances resilience evaluation by using dynamic convex risk measures.

Develops RL for dynamic risk assessment in stochastic optimization.

The main goal of this paper is to investigate under which conditions cash-subadditive convex dynamic risk measures are time-consistent. Proceeding as in Detlefsen and Scandolo \cite{detlef-scandolo} and inspired by their result, we give a dual representation of dynamic cash-subadditive convex risk measures (that can al…

We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an equivalent zero-sum game of control and stopping, between an agent (the "stopper") who c…

The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be integrated into the theoretical framework of convex monetary measures of risk. In …

Deep Hedging learns risk-neutral vol dynamics for option pricing.

Framework for quantifying uncertainty in dynamic processes.

Dynamic risk measures follow law invariance principles over time.

New conditional risk measures called conditional generalized quantiles defined and characterized.

Several authors have recently developed risk-sensitive policy gradient methods that augment the standard expected cost minimization problem with a measure of variability in cost. These studies have focused on specific risk-measures, such as the variance or conditional value at risk (CVaR). In this work, we extend the p…

In the context of an incomplete market with a Brownian filtration and a fixed finite time horizon, this paper proves that for general dynamic convex risk measures, the buyer's and seller's risk indifference prices of a contingent claim are bounded from below and above by the dynamic lower and upper hedging prices, resp…

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.

The paper explores non-convex risk measures and their characterizations.

The paper analyzes risk measures and optimal reserve allocation strategies.

We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for processes as introduced in Cheridito, Delbaen, and Kupper (2006). These risk measures take into account not only the amounts but also the timing of a cash flow. We discuss their robust representation in terms of suitably p…

Paper studies convex risk measures linked to optimization.

Study cash-subadditive risk measures without quasi-convexity.

Novel framework for risk-sensitive reinforcement learning with robustness against uncertainty.

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 certainty equivalent to conditional acceptability indexes. We provide the characteriza…

The paper defines and implements risk-indifference pricing for American-style contingent claims.

Submodularity is studied for convex risk measures, including Expected Shortfall.

Paper introduces quasi-logconvex risk measures and their properties.

In this article, we look at the effect of volatility clustering on the risk indifference price of options described by Sircar and Sturm in their paper (Sircar, R., & Sturm, S. (2012). From smile asymptotics to market risk measures. Mathematical Finance. Advance online publication. doi:10.1111/mafi.12015). The indiffere…

We present an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities in a discrete time setup using theory of dynamic acceptability indices. In the first part of the paper we develop the theory of dynamic subscale invariant performance measures, on a general probability space…

Introduces GG-convex risk measures and derives their dual representations.

Study optimizes natural resource harvesting under model uncertainty using risk measures.

Unified framework for robust risk measures beyond convexity.

In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by Föllmer, Schied (2002). The dynamic optimization problem of finding a self-financing strategy that minimizes the …

New set-valued star-shaped risk measures introduced for better risk assessment.

In the present contribution we characterize law determined convex risk measures that have convex level sets at the level of distributions. By relaxing the assumptions in Weber (2006), we show that these risk measures can be identified with a class of generalized shortfall risk measures. As a direct consequence, we are …

Optimal hedging framework with variational preferences under convex risk measures.

Paper characterizes star-shaped risk measures and their properties.

We study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of monetary risk measures time-consistent if it assigns to a process of financial values …

In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where risk is measured according to convex risk measures, we establish that the problem…

Constructs new elicitable risk measures with multiplicative scoring functions.

Optimal risk sharing without convex preferences using aggregate convexity.

To provide a solid analytic foundation for the module approach to conditional risk measures, this paper establishes a complete random convex analysis over random locally convex modules by simultaneously considering the two kinds of topologies (namely the $(\varepsilon,λ)$--topology and the locally $L^0$-- convex topolo…

In this work we study the Lebesgue property for convex risk measures on the space of bounded càdlàg random processes ($\mathcal{R}^\infty$). Lebesgue property has been defined for one period convex risk measures in \cite{Jo} and earlier had been studied in \cite{De} for coherent risk measures. We introduce and study th…

A risk-neutral method is always used to price and hedge contingent claims in complete market, but another method based on utility maximization or risk minimization is wildly used in more general case. One can find all kinds of special risk measure in literature. In this paper, instead of using market modified risk meas…

The paper refines and generalizes worst-case law invariant convex risk measures.