Forecasting Bitcoin risk measures: A robust approach

Over the last few years, Bitcoin and other cryptocurrencies have attracted the interest of many investors, practitioners and researchers. However, little attention has been paid to the predictability of their risk measures. This paper compares the predictability of the one-step-ahead volatility and Value-at-Risk of Bitcoin using several volatility models. We also include procedures that take into account the presence of outliers and estimate the volatility and Value-at-Risk in a robust fashion. Our results show that robust procedures outperform non-robust ones when forecasting the volatility and estimating the Value-at-Risk. These results suggest that the presence of outliers plays an important role in the modelling and forecasting of Bitcoin risk measures.     

Relevant coherent measures of risk

We introduce and study the _f0$f_0$-relevance property of a coherent measure of risk on a positions vector space with vector ordering. We show that it is equivalent to a special no arbitrage condition on bounded positions spaces. Continuity from below leads to representations of _f0$f_0$-relevant coherent measures of risk based on equivalent functionals in Banach subspaces of the order dual. We define and describe _f0$f_0$-martingales in a lattice, and present a solution to the hedging price problem: the asset price process is an order convergent _f0$f_0$-martingale. Under the _f0$f_0$-relevance hypothesis we study the relationship between worst conditional mean and value at risk.     

Off-balance sheet activities and bank default-risk premia: A comparison of risk measures

This paper examines the market discipline of off-balance sheet activities on the default-risk premia of subordinated bank debt. The standard approach for determining whether market prices of subordinated debt reflect the risk of default is to regress the yield spread against accounting measures of bank risk. This approach may be inadequate because yield spreads are neither linear nor monotonic functions of bank risk. Moreover, the standard approach fails to consider that banks are regulated. This paper compares this approach and one where risk is measured with a contingent claims pricing model. Observed yields on subordinated bank debt over equivalent maturity treasuries are used to compute implied asset variances. OBS banking activities appear to reduce both linear risk-premia and implied asset variances. These results suggest that bank regulators may be overly concerned with the risk exposure of off-balance sheet banking activities.     

The restricted convex risk measures in actuarial solvency

In this article, we propose a class of convex risk measures defined on appropriate wedges of a space of financial positions which denote the cumulative surplus variables created by undertaking risks by either an insurance or a reinsurance company. The form of the wedge which is the domain of such a risk measure expresses the form of the company, and it is a subspace in the case of reinsurance companies and a cone in the case of the insurance companies. The value of such a risk measure on an insurance position denotes the capital that the corresponding company has to receive or to keep in advance so that it will not be exposed to risk due to this position. We prove some dual representation and continuity results being similar to the unrestricted case. Finally, we contribute to a decision theory related to the choice of a numeraire asset when the space in which the positions lie in is reflexive.     

Rank-ordering of risk preferences with conventional and discrete measures

When the functional form of utility is unknown, conventional measures of risk aversion are often approximated by applying a Taylor series expansion to expected utility. This is shown to produce counterintuitive rank-orderings of risk preferences for individuals who are willing to pay equal reservation prices in lotteries with different prizes. Moreover, individuals who are unwilling to participate in favorable lotteries may be incorrectly identified as having a finite aversion to risk. Correct orderings are obtained by applying a discrete measure of relative risk aversion. The contrast between the conventional and discrete measures is illustrated with data from three Dutch surveys.     

Forecasting risk measures using intraday and overnight information

Volatility forecasts are important for a number of practical financial decisions, such as those related to risk management. When working with high-frequency data from markets that operate during a reduced time, an approach to deal with the overnight return volatility is needed. In this context, we use heterogeneous autoregressions (HAR) to model the variation associated with the intraday activity, with distinct realized measures as regressors, and, to model the overnight returns, we use augmented GARCH type models. Then, we combine the HAR and GARCH models to generate forecasts for the total daily return volatility. In an empirical study, for returns on six international stock indices, we analyze the separate modeling approach in terms of its out-of-sample forecasting performance of daily volatility, Value-at-Risk and Expected Shortfall relative to standard models from the literature. In particular, the overall results are favorable for the separate modeling approach in comparison with some HAR models based on realized variance measures for the whole day and the standard GARCH model.     

A representation of decision by analogy

We give a representation of analogical reasoning in choice under uncertainty. A decision maker is faced with two decision problems, a familiar and a novel one. It is shown that, under assumptions that capture the salience of alignable differences in choice, the decision maker can be construed as choosing between acts in the novel decision problem as if drawing all likelihood information from a multi-valued correspondence between states of the world in the familiar domain and states of the world in the novel domain. The latter is interpreted as an analogy between the two decision problems, and the fuzziness of the analogy is related to revealed ambiguity in the novel decision problem.     

地下商场的火灾危险性分析与预防对策

对地下商场的火灾危险性进行了分析,为使地下商场安全运营,提出了预防地下商场火灾的基本措施及相应对策。     

Monetary risk measures for stochastic processes via Orlicz duality

Decisions in Economics and Finance - In this article, we extend the framework of monetary risk measures for stochastic processes to account for heavy tailed distributions of random cash flows...     

A reference-dependent representation with subjective tastes

Experimental and empirical evidence documents instances where the presence of an inferior option in a menu increases the attractiveness of the better options from that menu and thus distorts the normative ranking across menus. We analyze the case when in addition to this so called context-effects bias there is also a concern for flexibility, in the spirit of the literature initiated by Kreps (1979) and Dekel et al. (2001). Since the context-effects bias and the desire for flexibility both increase the inclination of a decision maker to choose larger menus, our analysis allows the disentangling of the effect of the behavioral bias from the effect of the rational desire from flexibility. We find a weak condition on the set of ex post preferences under which the two effects are identifiable. We show that our representation is essentially unique. From a methodological viewpoint, our paper provides a novel technique of identifying probabilities on the state space of subjective uncertainty introduced by Dekel et al. (2001) when this state space is infinite. This method renders the infinite state space essentially finite with respect to a certain salient property.     

Coherent risk measures in general economic models and price bubbles

In this article we study coherent risk measures in general economic models where the set of financial positions is an ordered Banach space E$E$ and the safe asset an order unit _x0$x_0$ of E$E$. First we study some properties of risk measures. We show that the set of normalized (with respect to _x0$x_0$) price systems is weak star compact and by using this result we prove a maximum attainment representation theorem which improves the one of Jaschke and Küchler (2001). Also we study how a risk measure changes under different safe assets and we show a kind of equivalence between these risk measures. In the sequel we study subspaces of E$E$ consisting of financial positions of risk greater or equal to zero and we call these subspaces unsure. We find some criteria and we give examples of these subspaces. In the last section, we combine the unsure subspaces with the theory of price-bubbles of Gilles and LeRoy (1992).     

Robust tracking error portfolio selection with worst-case downside risk measures

This paper proposes downside risk measure models in portfolio selection that captures uncertainties both in distribution and in parameters. The worst-case distribution with given information on the mean value and the covariance matrix is used, together with ellipsoidal and polytopic uncertainty sets, to build-up this type of downside risk model. As an application of the models, the tracking error portfolio selection problem is considered. By lifting the vector variables to positive semidefinite matrix variables, we obtain semidefinite programming formulations of the robust tracking portfolio models. Numerical results are presented in tracking SSE50 of the Shanghai Stock Exchange. Compared with the tracking error variance portfolio model and the equally weighted strategy, the proposed models are more stable, have better accumulated wealth and have much better Sharpe ratio in the investment period for the majority of observed instances.     

A numerical representation of preferences with intransitive indifference

It is shown that, under certain conditions on a preference relation on a subset X of R^m, there exist real-valued functions u and v on X such that x is preferred to y if and only if u(x)>v(y). This generalises the familiar representation of preferences by a utility function in the case where the preference and indifference relations are transitive. The continuity of the functions u and v is also discussed.     

A special representation of a sufficient randomization kernel

Summary A recent paper byKumar/Pathak [1977] contains two examples showing how—in the presence of a boundedly complete sufficient statistic—a randomization kernel can be obtained which yields a random variable equivalent to the original one.It is the purpose of this note to present a simple general theorem containing these examples as special cases. The essential assumption is that the observation can be expressed by a pair of stochastically independent statistics, one of which is ancillary.     

Rates of almost sure convergence of plug-in estimates for distortion risk measures

In this article, we consider plug-in estimates for distortion risk measures as for instance the Value-at-Risk, the Expected Shortfall or the Wang transform. We allow for fairly general estimates of the underlying unknown distribution function (beyond the classical empirical distribution function) to be plugged in the risk measure. We establish strong consistency of the estimates, we investigate the rate of almost sure convergence, and we study the small sample behavior by means of simulations.     

跨组织物流成本管理的风险因素与防范对策研究

随着供应链的进一步发展,企业的物流成本管理从单一企业物流成本控制转变为由多个企业组成的跨组织物流成本管理。这种管理模式的出现,为企业的成本管理提出了新的要求和思路。文中分析了跨组织成本管理的内涵与特点,在分析其面临风险的基础上,提出了相应的防范对策。     

How HR measures support risk management: The Deutsche bank example

Are there concrete examples of how the “soft” HR factors can be made tangible and, what's more, meaningful to the business? In this article we give an answer to this frequently asked question. We show how Deutsche Bank's HR function consistently developed the range of employee surveying instruments to become pivotal to the Group's success. This is part of a wider effort in recent years to achieve a change of direction for the HR function, making it a strategic partner to the business. © 2002 Wiley Periodicals, Inc.     

Optimal portfolio selection via conditional convex risk measures on L p

We consider conditional convex risk measures on L ^p and show their robust representation in a standard way. Such measures are used as evaluation functionals for optimal portfolio selection in a Black&Scholes setting. We study this problem focusing on the conditional Average Value at Risk and the conditional entropic risk measure and compare the respective optimizers.     

A numerical representation of semiorders on a countable set

Let be a semiorder on a countable setX and letx⁰ y if and only if either there existsx withxxy or there existsx withxxy. Then ⁰ is a preference relation with transitive indifference, which can be represented by a utility functionf of the usual sort. It is well known that is represented by a pair of real-valued functionsu, v, in the sense thatxy if and only ifu(x)>v(y). We prove that there exists a pair of functionsu, v, representing , such thatu+v is the utility function which represents in the usual sense. Moreover it is easily seen that, for such a pair of functionsu, v, we havex⁰ y if and only if eitheru(x)>u(y) or (u(x)=u(y) andv(x)>v(y)).

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Sommario Consideriamo unsemiordine su un insiemeX numerabile e poniamox⁰ y se e solo se esistex tale chexxy, oppure esistex tale chexxy. In questo caso ⁰ è unordine debole, che può essere rappresentato da una funzione di utilitàf nel senso usuale. D'altra parte è rappresentato da una coppia di funzioniu, v, nel senso chexy se e solo seu(x)>v(y). In questo lavoro si prova che ammette una rappresentazioneu, v tale chex⁰ y se e solo seu(x)+v(x)>u(y)+v(y). Si dimostra altresì che, con riguardo ad una siffatta rappresentazioneu, v di , riescex⁰ y se e solo seu(x)>u(y) oppure (u(x)=u(y) ed anchev(x)>v(y)).