Risk Management & Tail Risk

A theoretical model of systemic-risk propagation of financial market is analyzed for stability. The state equation is an unsteady diffusion equation with a nonlinear logistic growth term, where the diffusion process captures the spread of default stress between interconnected financial entities and

We study Pareto-optimal risk sharing in economies with heterogeneous attitudes toward risk, where agents’ preferences are modeled by distortion risk measures. Building on comonotonic and counter-monotonic improvement results, we show that agents with similar attitudes optimally share risks comonoton

We propose the Financial Connectome, a new scientific discipline that models financial markets through the lens of brain functional architecture. Inspired by the foundational work of group independent component analysis (groupICA) in neuroscience, we reimagine markets not as collections of assets, b

The research investigates how the application of a machine-learning random forest model improves the accuracy and precision of a Delphi model. The context of the research is Azerbaijani SMEs and the data for the study has been obtained from a financial institution which had gathered it from the ente

Fairness in decision-making processes is often quantified using probabilistic metrics. However, these metrics may not fully capture the real-world consequences of unfairness. In this article, we adopt a utility-based approach to more accurately measure the real-world impacts of decision-making proce

Calculating true volatility is an essential task for option pricing and risk management. However, it is made difficult by market microstructure noise. Particle filtering has been proposed to solve this problem as it favorable statistical properties, but relies on assumptions about underlying market

The real options approach is now considered an effective alternative to the corporate DCF model for a feasibility study. The current paper offers a practical methodology employing binomial trees and real options techniques for evaluating investment projects. A general computation procedure is sugges

These are my Lecture Notes for a course in Discrete Time Finance which I taught in the Winter term 2005 at the University of Leeds. I am aware that the notes ar

In the context of micro-finance, a group of individuals undertake business projects that may interfere with one another. A contagious default happens if one person’s project failure leads to the default of another group member. In this paper, we apply a probabilistic approach to analyze the impact o

We consider a competitive market with risk-averse participants. We assume that agents’ risks are measured by coherent risk measures introduced by Artzner et al. (1999). Fundamental theorems of welfare economics have long established the equivalence of competitive equilibria and system welfare optimi

In this paper, we will show that under certain conditions, associated to any fixed distortion function $g$, the distortion risk measure of a sum of two counter-monotonic risks can be expressed as the sum of two related distortion risk measures of the marginals involved, one associated to the origina

The Basel Committee on Banking Supervision proposed replacing all approaches for operational risk capital, including the Advanced Measurement Approach (AMA), with a simplified formula called the Standardized Measurement Approach (SMA). This paper examines and criticizes the weaknesses and failures o

With the development of the financial industry, credit default prediction, as an important task in financial risk management, has received increasing attention. Traditional credit default prediction methods mostly rely on machine learning models, such as decision trees and random forests, but these

Financial markets are often modelled as if time were unique and continuous across assets and markets. Financial markets are however asynchronous, order flow is event-driven, and waiting times between events are often random. Many of the most influential formulations of financial market models presup

Stablecoins have emerged as a significant component of global financial infrastructure, with aggregate market capitalization surpassing USD250 billion in 2025. Their increasing integration into payment and settlement systems has simultaneously introduced novel channels of systemic exposure, particul

I propose a functional on the space of spectral risk measures that quantifies their degree of risk aversion''. This quantification formalizes the idea that some risk measures are more risk-averse’’ than others. I construct the functional using two axioms: a normalization on the space of CVaRs an

This mini-project models propagation of shocks, in time point, through links in connected banks. In particular, financial network of 100 banks out of which 15 are shocked to default (that is, 85.00% of the banks are solvent) is modelled using Erdos and Renyi network – directed, weighted and randomly

Risk measures satisfying the axiom of comonotonic additivity are extensively studied, arguably because of the plethora of results indicating interesting aspects of such risk measures. Recent research, however, has shown that this axiom is incompatible with central properties in specific contexts. In

The integration of cryptocurrencies into institutional portfolios necessitates the adoption of robust risk modeling frameworks. This study is a part of a series of subsequent works to fine-tune model risk analysis for cryptocurrencies. Through this first research work, we establish a foundational be

We investigate the ordering between two fundamental measures of dispersion for real-valued risks: the standard deviation (SD) and the Gini mean difference (GMD). Our analysis is driven by a single structural object, namely the mean excess function of the pairwise difference $|X - X’|$. We show that