Change-point detection for expected shortfall in time series

Expected shortfall (ES) is a popular risk measure and plays an important role in risk and portfolio management. Recently, change-point detection of risk measures has been attracting much attention in finance. Based on the self-normalized CUSUM statistic in Fan, Glynn and Pelger (2018) and the Wild Binary Segmentation (WBS) algorithm in Fryzlewicz (2014), this paper proposes a variant WBS procedure to detect and estimate change points of ES in time series. The strengthened Schwarz information criterion is also introduced to determine the number of change points. Monte Carlo simulation studies are conducted to assess the finite-sample performance of our variant WBS procedure about ES in time series. An empirical application is given to illustrate the usefulness of our procedure.     

A NOTE ON ARBITRAGE AND CLOSED CONVEX CONES

We give an example of a subspace K of     such that     , where     denotes the closure with respect to convergence in probablity. On the other hand, the cone   C ≔ K − L ^∞₊  is dense in   L ^∞  with respect to the weak-star topology  σ( L ^∞, L ¹)  . This example answers a question raised by I. Evstigneev. The topic is motivated by the relation of the notion of no arbitrage and the existence of martingale measures in Mathematical Finance.     

Sanov meets Cramér again

We introduce a new method for proving large-deviation principles (LDPs). This method amounts to "mixing" a collection of LDPs with a sequence of probability measures that obeys itself an LDP. As an illustration, we construct from empirical measures a sequence of capacity-valued maps that can be considered as an indexed collection of LDPs. The index 1 coincides with Sanov's theorem. By taking a Poisson mixture we establish a new connection with Cramér's theorem.     

Another view on optimal design for estimating the point of extremum in quadratic regression

In this paper we illustrate how certain design problems can be simplified by reparametrization of the response function. This alternative viewpoint provides further insights than the more traditional approaches, like minimax, Bayesian or sequential techniques. It will also improve a practitioner’s understanding of more general situations and their “classical” treatment.     

随机存货决策中的安全库存研究

在有短缺成本下 ,讨论了再定购点的确定 ,着重分析了安全库存的一种简易计算。     

Rethinking the role of NCBs in the EMU

Five years after the introduction of unified monetary policy in the EMU, some member countries are wondering whether they have ceded too much of their policy-making powers. The fact that National Central Banks no longer carry out sizable expansionary open market or foreign exchange market operations suggests that they face substantially reduced abilities to set economic policy.This paper demonstrates that, in fact, very little power has been yielded: on the fiscal front, the force of such policy initiatives is enhanced by the fixity of the exchange rate. On the monetary front, we show that there is an observational equivalence between all Central Bank actions under fixed exchange rates. This implies that the authorities retain the same amount of policy flexibility as before. So long as they use an alternative form of policy initiative, carrying out what previously would have been characterized as sterilized foreign exchange market operations, their ability to influence the macro performance of their economy is undiminished.     

The mean-variance investment problem in a constrained financial market

This paper extends the mean-variance analysis and the two-fund separation theorem to a market with some constraints, such as, the incompleteness, prohibition of short-selling, and partial information, with stochastic interest rate, and with stochastic volatility for risky assets. By maximizing a quadratic utility of terminal wealth, we show that the efficient frontier for the problem is a straight line in the mean-standard-deviation diagram. The quadratic utility function exhibits mean-variance efficiency. Our results apply to portfolios of claims in a single period, multiperiod, and continuous time.     

密绕载流无限长螺线管管外的磁场

对于密绕载流无限长螺线管,管外的磁场是否严格为零与管外磁场和管内磁场相比是否可以忽略不计,这是两个完全不同的问题。     

Conditioning as disintegration

Conditional probability distributions seem to have a bad reputation when it comes to rigorous treatment of conditioning. Technical arguments are published as manipulations of Radon–Nikodym derivatives, although we all secretly perform heuristic calculations using elementary definitions of conditional probabilities. In print, measurability and averaging properties substitute for intuitive ideas about random variables behaving like constants given particular conditioning information.
One way to engage in rigorous, guilt-free manipulation of conditional distributions is to treat them as disintegrating measures—families of probability measures concentrating on the level sets of a conditioning statistic. In this paper we present a little theory and a range of examples—from EM algorithms and the Neyman factorization, through Bayes theory and marginalization paradoxes—to suggest that disintegrations have both intuitive appeal and the rigor needed for many problems in mathematical statistics.