Related papers: Measuring Financial Resilience Using Backward Stoc…
In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present…
We examine the sensitivity properties of backward stochastic differential equations and reflected backward stochastic differential equations, which naturally arise in the context of optimal control and optimal stopping problems. Motivated…
Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
Comparable to the traditional notion of stability in system dynamics, resilience is typically measured in a way that assesses the quality of a system's response, for example the speed of its recovery. We present a broadly applicable…
Classical measures of structural reliability, such as the probability of failure and the related reliability index, are still widely applied in practice. However, these measures are frequency-based only, and they do not give information…
Prediction of post-loan default is an important task in credit risk management, and can be addressed by detection of financial anomalies using machine learning. This study introduces a ResE-BiLSTM model, using a sliding window technique,…
We analyze the relative price change of assets starting from basic supply/demand considerations subject to arbitrary motivations. The resulting stochastic differential equation has coefficients that are functions of supply and demand. We…
In this paper, we derive a representation for the value process associated to the solutions of FBSDEs in a jump-diffusion setting under multiple probability measures. Motivated by concrete financial problems, the latter representations are…
In this paper, we introduce a new type of backward stochastic differential equations (BSDEs) with infinite anticipation, where the generator depends on the entire future values of the solution in infinite horizon. We show that the new BSDEs…
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…
The purpose of this paper is to describe and extend the use of the newly-introduced measure, residual estimation risk. Following the seminal work of Bignozzi and Tsanakas, the quantification of residual estimation risk is proposed in a…
In this paper, we study a multidimensional backward stochastic differential equation (BSDE) with an additional rough drift (rough BSDE), and give the existence and uniqueness of the adapted solution, either when the terminal value and the…
In this paper, we study reflected backward stochastic difference equations (RBSDEs for short) with finitely many states in discrete time. The general existence and uniqueness result, as well as comparison theorems for the solutions, are…
Due to the variety of corporate risks in turmoil markets and the consequent financial distress especially in COVID-19 time, this paper investigates corporate resilience and compares different types of resilience that can be potential…
We consider the problem of governing systemic risk in an assets-liabilities dynamical model of banking system. In the model considered each bank is represented by its assets and its liabilities.The capital reserves of a bank are the…
In theoretical studies, the most commonly used measure of ecological stability is resilience: ecosystems asymptotic rate of return to equilibrium after a pulse-perturbation $-$or shock. A complementary notion of growing popularity is…
Despite the significant advances in deep learning over the past decade, a major challenge that limits the wide-spread adoption of deep learning has been their fragility to adversarial attacks. This sensitivity to making erroneous…
In this paper, we consider a risk-averse decision problem for controlled-diffusion processes, with dynamic risk measures, in which multiple risk-averse agents choose their decisions in such a way to minimize their individual accumulated…
This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from…