Related papers: Time consistency for scalar multivariate risk meas…
Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic…
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…
In a dynamic framework, we identify a new concept associated with the risk of assessing the financial exposure by a measure that is not adequate to the actual time horizon of the position. This will be called horizon risk. We clarify that…
The inversion formula for conservative multifractal measures was unveiled mathematically a decade ago, which is however not well tested in real complex systems. In this Letter, we propose to verify the inversion formula using high-frequency…
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price…
Monitoring downside risk and upside risk to the key macroeconomic indicators is critical for effective policymaking aimed at maintaining economic stability. In this paper I propose a parametric framework for modelling and forecasting…
Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…
In this paper, we consider a risk-averse decision problem for controlled-diffusion processes, with dynamic risk measures, in which there are two risk-averse decision makers (i.e., {\it leader} and {\it follower}) with different risk-averse…
In this paper we solve the discrete time mean-variance hedging problem when asset returns follow a multivariate autoregressive hidden Markov model. Time dependent volatility and serial dependence are well established properties of financial…
We give an axiomatic framework for conditional generalized deviation measures. Under financially reasonable assumptions, we give the correspondence between conditional coherent risk measures and generalized deviation measures. Moreover, we…
In the past few decades considerable effort has been expended in characterizing and modeling financial time series. A number of stylized facts have been identified, and volatility clustering or the tendency toward persistence has emerged as…
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…
We provide analytical results for a static portfolio optimization problem with two coherent risk measures. The use of two risk measures is motivated by joint decision-making for portfolio selection where the risk perception of the portfolio…
In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability $\alpha$, the $100\alpha\%$ VaR is…
Risk assessment under different possible scenarios is a source of uncertainty that may lead to concerning financial losses. We address this issue, first, by adapting a robust framework to the class of spectral risk measures. Second, we…
This paper discusses a nonlinear integral equation arising from portfolio selection with a class of time-inconsistent preferences. We propose a unified framework requiring minimal assumptions, such as right-continuity of market coefficients…
Empirical studies indicate the presence of multi-scales in the volatility of underlying assets: a fast-scale on the order of days and a slow-scale on the order of months. In our previous works, we have studied the portfolio optimization…
In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider…
A classical result in risk measure theory states that every coherent risk measure has a dual representation as the supremum of certain expected value over a risk envelope. We study this topic in more detail. The related issues include: 1.…
Financial markets tend to switch between various market regimes over time, making stationarity-based models unsustainable. We construct a regime-switching model independent of asset classes for risk-adjusted return predictions based on…