Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Cash non-additive risk measures: horizon risk and generalized entropy

Horizon risk (see arXiv:2301.04971) is studied in the context of cash non-additive fully-dynamic risk measures induced by BSDEs. Furthermore, we introduce a risk measure based on generalized Tsallis entropy which can dynamically evaluate the riskiness of losses considering both horizon risk and inte

Lab Rats Math 8.5 Rigor 2.5 ·  January 25, 2024

Measuring Financial Resilience Using Backward Stochastic Differential Equations

We introduce the resilience rate as a measure of financial resilience. It captures the expected rate at which a dynamic risk measure recovers, i.e., bounces back, when the risk-acceptance set is breached. We develop the corresponding stochastic calculus by establishing representation theorems for ex

Lab Rats Math 9 Rigor 2 ·  May 12, 2025

Geometric BSDEs

We introduce and develop the concepts of Geometric Backward Stochastic Differential Equations (GBSDEs, for short) and two-driver BSDEs. We demonstrate their natural suitability for modeling continuous-time dynamic return risk measures. We characterize a broad spectrum of associated, auxiliary ordina

Lab Rats Math 9.5 Rigor 1.5 ·  May 15, 2024

Dynamic Return and Star-Shaped Risk Measures via BSDEs

This paper establishes characterization results for dynamic return and star-shaped risk measures induced via backward stochastic differential equations (BSDEs). We first characterize a general family of static star-shaped functionals in a locally convex Fréchet lattice. Next, employing the Pasch-Hau

Lab Rats Math 9.5 Rigor 1.5 ·  July 7, 2023

Are Shortfall Systemic Risk Measures One Dimensional?

Shortfall systemic (multivariate) risk measures $ρ$ defined through an $N$-dimensional multivariate utility function $U$ and random allocations can be represented as classical (one dimensional) shortfall risk measures associated to an explicitly determined $1$-dimensional function constructed from $

Lab Rats Math 8.5 Rigor 2 ·  June 19, 2023

Law-Invariant Return and Star-Shaped Risk Measures

This paper presents novel characterization results for classes of law-invariant star-shaped functionals. We begin by establishing characterizations for positively homogeneous and star-shaped functionals that exhibit second- or convex-order stochastic dominance consistency. Building on these characte

Lab Rats Math 9 Rigor 1.5 ·  October 30, 2023

Robust quasi-convex risk measures and applications

This paper develops a unified framework for the robustification of risk measures beyond the classical convex and cash-additive setting. We consider general risk measures on Lp spaces and construct their robust counterparts through families of uncertainty sets that capture ambiguity. Two complementar

Lab Rats Math 8.5 Rigor 1.5 ·  March 18, 2026

Capturing cash non-additivity and horizon risk via BSDEs and generalized shortfall

Whenever dealing with horizons of different times scales, risk evaluation of losses may incur in both interest rate uncertainty and horizon risk as introduced in [11]. With the goal to capture both effects, we work with cash subadditive fully-dynamic risk measures. In this work we consider such meas

Lab Rats Math 8.5 Rigor 1.5 ·  March 14, 2026

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