Related papers: A Supermartingale Relation for Multivariate Risk M…
The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes which is, for continuous semimartingales, related to symmetry properties of both their ordinary as well as…
Consider an insurance company exposed to a stochastic economic environment that contains two kinds of risk. The first kind is the insurance risk caused by traditional insurance claims, and the second kind is the financial risk resulting…
The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves…
The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes, when deflated by it, supermartingales. The numeraire portfolio depends on market characteristics, which…
We characterize the event of convergence of a local supermartingale. Conditions are given in terms of its predictable characteristics and quadratic variation. The notion of stationarily local integrability plays a key role.
Given the univariate marginals of a real-valued, continuous-time martingale, (respectively, a family of measures parameterised by $t \in [0,T]$ which is increasing in convex order, or a double continuum of call prices) we construct a family…
We study coherent risk measures which are time-consistent for multiple filtrations. We show that a coherent risk measure is time-consistent for every filtration if and only if it is one of four main types. Furthermore, if the risk measure…
Portfolio selection in the periodic investment of securities modeled by a multivariate Merton model with dependent jumps is considered. The optimization framework is designed to maximize expected terminal wealth when portfolio risk is…
Given a c\`adl\`ag process $X$ on a filtered measurable space, we construct a version of its semimartingale characteristics which is measurable with respect to the underlying probability law. More precisely, let $\mathfrak{P}_{sem}$ be the…
We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and…
This paper compares two different frameworks recently introduced in the literature for measuring risk in a multi-period setting. The first corresponds to applying a single coherent risk measure to the cumulative future costs, while the…
We obtain some maximal probability and moment inequalities for multidimensionally indexed demimartingales. Although the class of single-indexed demimartingales has been studied extensively, no significant amount of work has been done for…
We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization. We model uncertainty in terms of the Gelbrich distance on the mean-covariance space, along with prior structural information about…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure…
Markov switching models are often used to analyze financial returns because of their ability to capture frequently observed stylized facts. In this paper we consider a multivariate Student-t version of the model as a viable alternative to…
Although stochastic volatility and GARCH (generalized autoregressive conditional heteroscedasticity) models have successfully described the volatility dynamics of univariate asset returns, extending them to the multivariate models with…
We consider a class of semi-Markov processes (SMP) such that the embedded discrete time Markov chain may be non-homogeneous. The corresponding augmented processes are represented as semi-martingales using stochastic integral equation…
Motivated by recent developments in the calibration of stochastic volatility models (SVMs for short), we study continuous-time formulations of martingale optimal transport and martingale Schr\"odinger bridge problems. We establish duality…
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…