Related papers: A Stochastic Processes Toolkit for Risk Management
This paper studies the estimation of characteristic-based quantile factor models where the factor loadings are unknown functions of observed individual characteristics while the idiosyncratic error terms are subject to conditional quantile…
Effective utilization of time series data is often constrained by the scarcity of data quantity that reflects complex dynamics, especially under the condition of distributional shifts. Existing datasets may not encompass the full range of…
There are various metrics for financial risk, such as value at risk (VaR), expected shortfall, expected/unexpected loss, etc. When estimating these metrics, it was very common to assume Gaussian distribution for the asset returns, which may…
Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state…
Temporal logics provide a formalism for expressing complex system specifications. A large body of literature has addressed the verification and the control synthesis problem for deterministic systems under such specifications. For…
In order to properly manage risk, practitioners must understand the aggregate risks they are exposed to. Additionally, to properly price policies and calculate bonuses the relative riskiness of individual business units must be well…
We examine a variety of graphical models to construct optimal portfolios. Graphical models such as PCA-KMeans, autoencoders, dynamic clustering, and structural learning can capture the time varying patterns in the covariance matrix and…
Identifying systemic risk patterns in geopolitical, economic, financial, environmental, transportation, epidemiological systems and their impacts is the key to risk management. This paper proposes a new nonlinear time series model:…
Credit risk stress testing has become an important risk management device which is used both by banks internally and by regulators. Stress testing is complex because it essentially means projecting a bank's full balance sheet conditional on…
There is a great number of factors to take into account when building and managing an investment portfolio. It is widely believed that a proper set-up of the portfolio combined with a good, robust management strategy is the key to…
In this paper, we consider the problem of extraction of most informative features from time series that are regarded as observed values of stochastic processes satisfying the It{\^{o}} stochastic differential equations with unknown random…
In modern science, computer models are often used to understand complex phenomena, and a thriving statistical community has grown around analyzing them. This review aims to bring a spotlight to the growing prevalence of stochastic computer…
Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each…
We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to managing the Value at Risk (VaR) assuming a heavy tailed distribution of…
We give an overview of several aspects arising in the statistical analysis of extreme risks with actuarial applications in view. In particular it is demonstrated that empirical process theory is a very powerful tool, both for the asymptotic…
The ongoing concern about systemic risk since the outburst of the global financial crisis has highlighted the need for risk measures at the level of sets of interconnected financial components, such as portfolios, institutions or members of…
We study the temporal robustness of stochastic signals. This topic is of particular interest in interleaving processes such as multi-agent systems where communication and individual agents induce timing uncertainty. For a deterministic…
Reliable calculations of financial risk require that the fat-tailed nature of prices changes is included in risk measures. To this end, a non-Gaussian approach to financial risk management is presented, modeling the power-law tails of the…
The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the…
A Value-at-Risk based model is proposed to compute the adequate equity capital necessary to cover potential losses due to operational risks, such as human and system process failures, in banking organizations. Exploring the analogy to a…