Risk Management & Tail Risk

We introduce the concept of set risk measures (SRMs), which are real-valued maps defined on the space of all non-empty, closed, and bounded sets of almost surely bounded random variables. Traditional risk measures typically operate on random variables, but SRMs extend this framework to sets of rando

Entropic Value-at-Risk (EVaR) measure is a convenient coherent risk measure. Due to certain difficulties in finding its analytical representation, it was previously calculated explicitly only for the normal distribution. We succeeded to overcome these difficulties and to calculate Entropic Value-at-

The paper provides a mathematical model and a tool for the focused investing strategy as advocated by Buffett, Munger, and others from this investment community. The approach presented here assumes that the investor’s role is to think about probabilities of different outcomes for a set of businesses

We provide a new characterization of second-order stochastic dominance, also known as increasing concave order. The result has an intuitive interpretation that adding a risk with negative expected value in adverse scenarios makes the resulting position generally less desirable for risk-averse agents

Automated market makers (AMMs) are pricing mechanisms utilized by decentralized exchanges (DEX). Traditional AMM approaches are constrained by pricing solely based on their own liquidity pool, without consideration of external markets or risk management for liquidity providers. In this paper, we pro

Recent advances in large language models, tool-using agents, and financial machine learning are shifting financial automation from isolated prediction tasks to integrated decision systems that can perceive information, reason over objectives, and generate or execute actions. This paper develops an i

Modern financial networks are highly connected and result in complex interdependencies of the involved institutions. In the prominent Eisenberg-Noe model, a fundamental aspect is clearing – to determine the amount of assets available to each financial institution in the presence of potential defaul

We study Stackelberg Equilibria (Bowley optima) in a monopolistic centralized sequential-move insurance market, with a profit-maximizing insurer who sets premia using a distortion premium principle, and a single policyholder who seeks to minimize a distortion risk measure. We show that equilibria ar

This work focuses on financial risks from a probabilistic point of view. The value of a firm is described as a geometric Brownian motion and default emerges as a first passage time event. On the technical side, the critical threshold that the value process has to cross to trigger the default is assu

This paper derives the best- and worst-case GlueVaR distortion risk measure within a unified framework, based on partial information of the underlying distributions and shape information such as symmetry. In addition, we characterize the extremal distributions of GlueVaR with convex envelopes of the

This paper takes the graph neural network as the technical framework, integrates the intrinsic connections between enterprise financial indicators, and proposes a model for enterprise credit risk assessment. The main research work includes: Firstly, based on the experience of predecessors, we select

Credit ratings are becoming one of the primary references for financial institutions of the country to assess credit risk in order to accurately predict the likelihood of business failure of an individual or an enterprise. Financial institutions, therefore, depend on credit rating tools and services

Project managers need to manage risks throughout the project lifecycle and, thus, need to know how changes in activity durations influence project duration and risk. We propose a new indicator (the Activity Risk Index, ARI) that measures the contribution of each activity to the total project risk wh

Since 2016 the operation of insurance companies in the European Union is regulated by the Solvency II directive. According to the EU directive the capital requirement should be calculated as a 99.5% of Value at Risk. In this study, we examine the impact of this capital requirement constraint on equ

The paper provides an overview of the theory and applications of risk-sensitive Markov decision processes. The term ‘risk-sensitive’ refers here to the use of the Optimized Certainty Equivalent as a means to measure expectation and risk. This comprises the well-known entropic risk measure and Condit

This paper introduces a novel approach to financial risk assessment by incorporating topological data analysis (TDA), specifically cohomology groups, into the evaluation of equities portfolios. The study aims to go beyond traditional risk measures like Value at Risk (VaR) and Conditional Value at Ri

This paper studies the links between the descriptions of macroeconomic variables and statistical moments of market trade, price, and return. The randomness of market trade values and volumes during the averaging interval Δ results in the random properties of price and return. We describe how average

We present simple general conditions on the acceptance sets under which their induced monetary risk and deviation measures are comonotonic additive. We show that acceptance sets induce comonotonic additive risk measures if and only if the acceptance sets and their complements are stable under convex

In this paper we formulate and solve an optimal problem for Stochastic process with a regime absorbing state. The solution for this problem is obtained through a system of partial differential equations. The method is applied to obtain an explicit solution for the Merton portfolio problem when an as

In financial and actuarial research, distortion and Haezendonck-Goovaerts risk measures are attractive due to their strong properties. They have so far been treated separately. In this paper, following a suggestion by Goovaerts, Linders, Van Weert, and Tank, we introduce and study a new class of ris