Risk Management & Tail Risk

In this paper, we present a methodology for measuring the impact of scenarios on the expected losses of exposures by leveraging the existing provisioning infrastructure within financial institutions, where scenario effects are captured through changes in probabilities of default. We then describe ho

The paper focuses heavily on risk management case studies, portfolio statistics, and drawdown analysis from LTCM’s historical data with specific return figures, but contains minimal advanced mathematics, relying mostly on descriptive statistics and historical narrative.

We consider a model for systemic risk comprising of a system of diffusion processes, interacting through their empirical mean. Each process is subject to a confining double-well potential with some uncertainty in the coefficients, corresponding to fluctuations in height of the potential barrier sepe

We revisit the problem of portfolio selection, where an investor maximizes utility subject to a risk constraint. Our framework is very general and accommodates a wide range of utility and risk functionals, including non-concave utilities such as S-shaped utilities from prospect theory and non-convex

The frequent occurrence of natural disasters has posed significant challenges to society, necessitating the urgent development of effective risk management strategies. From the early informal community-based risk sharing mechanisms to modern formal index insurance products, risk management tools hav

We introduce a family of particle systems on sparse graphs where local interactions occur via hitting times, providing a dynamic and tractable model for default cascades in large sparsely-connected financial networks. Building on the framework of Lacker, Ramanan and Wu (2023), we extend convergence

In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp upper bounds of distortion riskmetrics and weighted entropy f

In this article, we employ a principal-agent model to analyze optimal contract design in a monopolistic reinsurance market under adverse selection with a continuum of insurer types. Instead of using the classical expected utility framework, we model each insurer’s risk preference through their VaR a

We consider the pricing and hedging of counterparty credit risk and funding when there is no possibility to hedge the jump to default of either the bank or the counterparty. This represents the situation which is most often encountered in practice, due to the absence of quoted corporate bonds or CDS

In recent years, the frequency and intensity of grid-ignited wildfires have increased significantly, leading to an elevated level of risk exposure to public safety and financial repercussions for electric utilities threatening their solvency. It is, therefore, imperative for electric utilities to ac

Significant progress has been made in automated problem-solving using societies of agents powered by large language models (LLMs). In finance, efforts have largely focused on single-agent systems handling specific tasks or multi-agent frameworks independently gathering data. However, the multi-agent

We study the tail asymptotics of the sum of two heavy-tailed random variables. The dependence structure is modeled by copulas with the so-called tail order property. Examples are presented to illustrate the approach. Further for each example we apply the main results to obtain the asymptotic expansi

Decentralized Finance (DeFi) money markets have seen explosive growth in recent years, with billions of dollars borrowed in various cryptocurrency assets. Key to the safety of money markets is the implementation of interest rates that determine the cost of borrowing, and govern counterparty exposure

We study Pareto efficiency in a pure-exchange economy where agents’ preferences are represented by risk-averse monetary utilities. These coincide with law-invariant monetary utilities, and they can be shown to correspond to the class of monotone, (quasi-)concave, Schur concave, and translation-invar

The recent banking crisis has again emphasized the importance of understanding and mitigating systemic risk in financial networks. In this paper, we study a market-driven approach to rescue a bank in distress based on the idea of claims trading, a notion defined in Chapter 11 of the U.S. Bankruptcy

In this paper, we consider the discrete-time setting, and the market model described by (S,F,T)$. Herein F is the ``public" flow of information which is available to all agents overtime, S is the discounted price process of d-tradable assets, and T is an arbitrary random time whose occurrence might

We employ scoring functions, used in statistics for eliciting risk functionals, as cost functions in the Monge-Kantorovich (MK) optimal transport problem. This gives raise to a rich variety of novel asymmetric MK divergences, which subsume the family of Bregman-Wasserstein divergences. We show that

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 $

Focusing on gains & losses relative to a risk-free benchmark instead of terminal wealth, we consider an asset allocation problem to maximize time-consistently a mean-risk reward function with a general risk measure which is i) law-invariant, ii) cash- or shift-invariant, and iii) positively homogene

In this brief note, we prove that both forms of the Gerber statistic introduced in Gerber et al. (2022) are positive semi-definite.