Related papers: Default Risk Modeling Beyond the First-Passage App…
We study the initial-boundary value problem for the Fokker-Planck equation in an interval with absorbing boundary conditions. We develop a theory of well-posedness of classical solutions for the problem. We also prove that the resulting…
We consider a portfolio optimization problem in a defaultable market with finitely-many economical regimes, where the investor can dynamically allocate her wealth among a defaultable bond, a stock, and a money market account. The market…
In this paper, we study finite-time ruin probabilities for the compound Markov binomial risk model - a discrete-time model where claim sizes are modulated by a finite-state ergodic Markov chain. In the classic (non-modulated) case, the risk…
We formulate a short-time expansion for one-dimensional Fokker-Planck equations with spatially dependent diffusion coefficients, derived from stochastic processes with Gaussian white noise, for general values of the discretization parameter…
Credit risk assessment of a company is commonly conducted by utilizing financial ratios that are derived from its financial statements. However, this approach may not fully encompass other significant aspects of a company. We propose the…
Diffusion models play an essential role in modeling continuous-time stochastic processes in the financial field. Therefore, several proposals have been developed in the last decades to test the specification of stochastic differential…
From the data analysis we defined distribution function against the population on the level of various structure units, namely regions, federal districts and the country on the whole. We have studied peculiarities of the distribution…
A continuum model of crack propagation is presented and discussed. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic and viscoelastic effects are…
This paper extends the classical dividend problem by incorporating a novel, path-dependent mechanism of firm default. In the traditional framework, ruin occurs when the surplus process first reaches zero. In contrast, default in our model…
In this paper, we investigate a financial market model consisting of a risky asset, modeled as a general diffusion parameterized by a scale function and a speed measure, and a bank account process with a constant interest rate. This…
One of the most defining features of the global financial network is its inherent complex and intertwined structure. From the perspective of systemic risk it is important to understand the influence of this network structure on default…
In this paper, we introduce a model that adds a non-linearity to discounting: the discounting factor may depend on the notional (i.e., discounted values are no longer linear in the notional). In the first part of the paper, we provide a…
This study explores the integration of Blackout Diffusion into the DIFUSCO framework for combinatorial optimization, specifically targeting the Traveling Salesman Problem (TSP). Inspired by the success of discrete-time diffusion models…
This paper proposes a new extension of the linear failure rate (LFR) model to better capture real-world lifetime data. The model incorporates an additional shape parameter to increase flexibility. It helps model the minimum survival time…
We study a variant of the Cucker-Smale model where information between agents propagates with a finite speed $\mathfrak{c}>0$. This leads to a system of functional differential equations with state-dependent delay. We prove that, if…
Memory effects require for their incorporation into random-walk models an extension of the conventional equations. The linear Fokker-Planck equation for the probability density $p(\vec r, t)$ is generalized to include non-linear and…
The equity risk premium puzzle is that the return on equities has far exceeded the average return on short-term risk-free debt and cannot be explained by conventional representative-agent consumption based equilibrium models. We review a…
This chapter reviews key contributions of complexity science to the study of systemic risk in financial systems. The focus is on network models of financial contagion, where I explore various mechanisms of shock propagation, such as…
With the widespread application of machine learning in financial risk management, conventional wisdom suggests that longer training periods and more feature variables contribute to improved model performance. This paper, focusing on…
In this paper we present a novel model checking approach to finite-time safety verification of black-box continuous-time dynamical systems within the framework of probably approximately correct (PAC) learning. The black-box dynamical…