Related papers: The Temporal Dimension of Risk
In this paper we propose the notion of continuous-time dynamic spectral risk-measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk-measures in terms of certain backward stochastic…
We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase-transition occurs…
We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As it is well known, one can map this problem into a linear programming setting. For some values of the external…
A new approach is presented to describe the change in the statistics of the log return distribution of financial data as a function of the timescale. To this purpose a measure is introduced, which quantifies the distance of a considered…
We propose a new class of mappings, called Dynamic Limit Growth Indices, that are designed to measure the long-run performance of a financial portfolio in discrete time setup. We study various important properties for this new class of…
Choosing a portfolio of risky assets over time that maximizes the expected return at the same time as it minimizes portfolio risk is a classical problem in Mathematical Finance and is referred to as the dynamic Markowitz problem (when the…
Temporal correlations in quantum mechanics are the origin of several non-classical phenomena, but they depend on the dimension of the underlying quantum system. This allows one to use such correlations for the certification of a minimal…
This paper introduces an innovative framework for the periodic evaluation of defined-contribution pension funds. The performance of the pension fund is evaluated not only at retirement, but also within the interim periods. In contrast to…
Accurate estimation for extent of cross{sectional dependence in large panel data analysis is paramount to further statistical analysis on the data under study. Grouping more data with weak relations (cross{sectional dependence) together…
Real world networks exhibit rich temporal information: friends are added and removed over time in online social networks; the seasons dictate the predator-prey relationship in food webs; and the propagation of a virus depends on the network…
Complexity measures are designed to capture complex behavior and quantify *how* complex, according to that measure, that particular behavior is. It can be expected that different complexity measures from possibly entirely different fields…
In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures, focusing on a the discrete time setup. The two key operational concepts used throughout are the notion of the…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
This paper approaches the definition and properties of dynamic convex risk measures through the notion of a family of concave valuation operators satisfying certain simple and credible axioms. Exploring these in the simplest context of a…
By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be…
Multi-layered networks represent a major advance in the description of natural complex systems, and their study has shed light on new physical phenomena. Despite its importance, however, the role of the temporal dimension in their structure…
In this paper we study time-consistent risk measures for returns that are given by a GARCH(1,1) model. We present a construction of risk measures based on their static counterparts that overcomes the lack of time-consistency. We then study…
We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a…
Value at risk (VaR) and expected shortfall (ES) are common high quantile-based risk measures adopted in financial regulations and risk management. In this paper, we propose a tail risk measure based on the most probable maximum size of risk…
The new notion of maturity-independent risk measures is introduced and contrasted with the existing risk measurement concepts. It is shown, by means of two examples, one set on a finite probability space and the other in a diffusion…