Compound poisson models in actuarial risk theory

This paper deals with the relationship between the Compound Poisson distribution, Bayesian uncertainty (or mixing) models and infinite divisibility. It is shown that the Compound Poisson distribution arises in many situations in the theory of risk. A large number of recent results are reviewed and some new results are given.     

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.     

Equal risk pricing under convex trading constraints

In an incomplete market model where convex trading constraints are imposed upon the underlying assets, it is no longer possible to obtain unique arbitrage-free prices for derivatives using standard replication arguments. Most existing derivative pricing approaches involve the selection of a suitable martingale measure or the optimisation of utility functions as well as risk measures from the perspective of a single trader.We propose a new and effective derivative pricing method, referred to as the equal risk pricing approach, for markets with convex trading constraints. The approach analyses the risk exposure of both the buyer and seller of the derivative, and seeks an equal risk price which evenly distributes the expected loss for both parties under optimal hedging. The existence and uniqueness of the equal risk price are established for both European and American options. Furthermore, if the trading constraints are removed, the equal risk price agrees with the standard arbitrage-free price.Finally, the equal risk pricing approach is applied to a constrained Black–Scholes market model where short-selling is banned. In particular, simple pricing formulas are derived for European calls, European puts and American puts.     

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.     

A representation of risk measures

We provide a representation theorem for risk measures satisfying (1) monotonicity, (2) positive homogeneity and (3) translation invariance. As a simple corollary to our theorem, we obtain the usual representation of coherent risk measures (i.e., risk measures that are, in addition, sub-additive; see Artzner et al. in Math Finance 9:203–228, 1999).     

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.     

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).     

The dominant firm with convex technology

The paper analyses a dominant firm model in which firms have convex production sets. The model is shown to be determinate, and to be expressible by a set of (n+1) equilibrium conditions. A previous attempt to obtain comparative statics results is criticized as being invalid, and a new framework for comparative statics is developed.     

Quadratic risk domination of restricted least squares estimators via Stein-ruled auxiliary constraints

This paper develops an estimator that under the standard assumption of the General Linear Model, including normality of disturbances, can be designed to dominate the Restricted Least Squares estimator in quadratic risk under very general conditions. The domination is achieved for any choice of symmetric positive definite weighting matrix used in defining the quadratic risk function, regardless of the correctness of the constraints used to define the restricted least squares estimator. The general problem conditions under which the estimator exists, and the risk behavior of the estimator over the parameter space are identified.     

Some problems in actuarial finance involving sums of dependent risks

A trend in actuarial finance is to combine technical risk with interest risk. If Y_t , t = 1, 2, denotes the timevalue of money (discount factors at time t ) and X_t the stochastic payments to be made at time t , the random variable of interest is often the scalar product of these two random vectors V = X_t Y_t . The vectors X and Y are supposed to be independent, although in general they have dependent components. The current insurance practice based on the law of large numbers disregards the stochastic financial aspects of insurance. On the other hand, introduction of the variables Y ₁, Y ₂, to describe the financial aspects necessitates estimation or knowledge of their distribution function.
We investigate some statistical models for problems of insurance and finance, including Risk Based Capital/Value at Risk, Asset Liability Management, the distribution of annuities, cash flow evaluations (in the framework of pension funds, embedded value of a portfolio, Asian options) and provisions for claims incurred, but not reported (IBNR).     

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.     

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.     

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...     

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 data in a generalized autoregressive score framework

A new framework for the joint estimation and forecasting of dynamic value at risk (VaR) and expected shortfall (ES) is proposed by our incorporating intraday information into a generalized autoregressive score (GAS) model introduced by Patton et al., 2019 to estimate risk measures in a quantile regression set-up. We consider four intraday measures: the realized volatility at 5-min and 10-min sampling frequencies, and the overnight return incorporated into these two realized volatilities. In a forecasting study, the set of newly proposed semiparametric models are applied to four international stock market indices (S&P 500, Dow Jones Industrial Average, Nikkei 225 and FTSE 100) and are compared with a range of parametric, nonparametric and semiparametric models, including historical simulations, generalized autoregressive conditional heteroscedasticity (GARCH) models and the original GAS models. VaR and ES forecasts are backtested individually, and the joint loss function is used for comparisons. Our results show that GAS models, enhanced with the realized volatility measures, outperform the benchmark models consistently across all indices and various probability levels.     

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.     

The predictive power of fund ratings with a novel approach using uncertainty measures to analyzing risk

Using two approaches to panel data, Granger causality analysis with semi-asymptotic tests, and a structural approach based on entropies measured on sequences of multiperiod ratings and returns, we specify the relationship between a fund’s performance and both Morningstar and Europerformance ratings. We conclude on the Europerformance agency’s forecasting ability for the Luxembourg funds, and the Morningstar agency for the French funds. Indeed, we find two groups of funds depending on their domiciliation and appropriated rating. The results of this paper have implications for the management of fund portfolios, and the structural approach, more robust to our data, must be a first process for forecast models on the basis of similar funds, minor uncertainty or risk measure, and appropriated rating.     

Fractional mortality rate based on rational interpolating method and its application in actuarial science

This paper attempts to introduce a new method with adjustable parameter for estimating the mortality of fractional age based on rational interpolating theory. The efficiency analysis of the method is given and some conditions the adjustable parameter should satisfy are given in order to meet the need of actuarial practice. We also analyze the relationship between our estimating method and the one based on UDD assumption—the most commonly used in actuarial study and practice. The result shows that the latter is just a special case of our results. Finally we apply our method to the calculations of actuarial present value of life insurance and annuities. Simulations are also done to give a clear comparison between traditional method and our method specified in this paper.