A Novel DBN-EFA-CFA-Based Dimensional Reduation for Credit Risk Measurement

Affected by the Federal Reserve's interest rate hike and the downward pressure on the domestic economy,the phenomenon of default is still prominent.The credit risk of the listed companies has become a growing concern of the community.In this paper we present a novel credit risk measurement method based on a dimensional reduation technique.The method first extracts the risk measure indexes from the basal financial data via dimensional reduation by using deep belief network(DBN),exploratory factor analysis(EFA)and confirmatory factor analysis(CFA)in turn.And then the credit risk is measured by a systemic structural equation model(SEM)and logistic distribution.To validate the proposed method,we employ the financial data of the listed companies from Q12019 to Q22022.The empirical results show its effectiveness on statistical evaluation,assessment on testing samples and credit risk forecasting.

ANTICIPATED BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS WITH JUMPS AND APPLICATIONS TO DYNAMIC RISK MEASURES

In this paper, we focus on anticipated backward stochastic Volterra integral equations(ABSVIEs) with jumps. We solve the problem of the well-posedness of so-called M-solutions to this class of equation, and analytically derive a comparison theorem for them and for the continuous equilibrium consumption process. These continuous equilibrium consumption processes can be described by the solutions to this class of ABSVIE with jumps.Motivated by this, a class of dynamic risk measures induced by ABSVIEs with jumps are discussed.

Construction Technology and Safety Risk Control Measures of Deep Foundation Pit Excavation

Deep foundation pit excavation is a basic and key step involved in modern building construction.In order to ensure the construction quality and safety of deep foundation pits,this paper takes a project as an example to analyze deep foundation pit excavation technology,including the nature of this construction project,the main technical measures in the construction of deep foundation pit,and the analysis of the safety risk prevention and control measures.The purpose of this analysis is to provide scientific reference for the construction quality and safety of deep foundation pits.

CASH SUBADDITIVE RISK MEASURES FOR PORTFOLIO VECTORS

In this paper, from the viewpoint of the time value of money, we study the risk measures for portfolio vectors with discount factor. Cash subadditive risk measures for portfolio vectors are proposed. Representation results are given by two different methods which are convex analysis and enlarging space. Especially, the method of convex analysis make the line of reasoning and the representation result be simpler. Meanwhile, spot and forward risk measures for portfolio vectors are also introduced, and the relationships between them are investigated.

Risk measures with comonotonic subadditivity or convexity on product spaces

In this paper, by an axiomatic approach, we propose the concepts of comonotonic subadditivity and comonotonic convex risk measures for portfolios, which are extensions of the ones introduced by Song and Yan （2006）. Representation results for these new introduced risk measures for portfolios are given in terms of Choquet integrals. Links of these newly introduced risk measures to multi-period comonotonic risk measures are represented. Finally, applications of the newly introduced comonotonic coherent risk measures to capital allocations are provided.

Value-at-risk under ambiguity aversion

This study explored the effects of ambiguity on the calculation of Value-at-Risk(VaR)using a mathematical model based on the theory of Choquet-Brownian processes.It was found that while a moderate degree of ambiguity aversion yields a higher value for VaR and Expected Shortfall(ES),the result can be reversed in a deeply ambiguous environment.Additionally,some sufficient conditions are provided for the preservation of this effect under various forms of risk aggregation.This study offers a new perspective to full awareness on capital requirement calculation as requested by international regulation.

On the generalized risk measures

In this paper, new risk measures are introduced, tation results are also given. These newly introduced risk introduced by Song and Yan （2009） and Karoui （2009）. and the corresponding represen- measures are extensions of those

Risk Measure and Premium Distribution on Catastrophe Reinsurance

In this paper, we propose a new risk measure which is based on the Or- licz premium principle to characterize catastrophe risk premium. The intention is to develop a formulation strategy for Catastrophe Fund. The logarithm equivalent form of reinsurance premium is regarded as the retention of reinsurer, and the differential earnings between the reinsurance premium and the reinsurer＇s retention is accumu- lated as a part of Catastrophe Fund. We demonstrate that the aforementioned risk measure has some good properties, which are further confirmed by numerical simu- lations in R environment.

Claim reserving for insurance contracts in line with the International Financial Reporting Standards 17:a new paid‑incurred chain approach to risk adjustments

This study considers the risk management of insurance policies in line with the implementation of the new International Financial Reporting Standards 17.It applies the paid-incurred chain method to model the future unpaid losses by combining the information channels of both the incurred claims and paid losses.We propose the recovery of the empirical distribution of the outstanding claims liabilities associated with a group of contracts via moment-based density approximation.We determine the risk measures and adjustments that are compliant with the new standard using the Monte–Carlo simulation method and approximated distributions.The historical data on the aggregate Ontario automobile insurance claims over a 15-year period are analyzed to examine the appropriateness and accuracy of our approach.

Best Bounds on Measures of Risk and Probability of Ruin for Alpha Unimodal Random Variables When There Is Limited Moment Information

This paper presents explicit formulae giving tight upper and lower bounds on the expectations of alpha-unimodal random variables having a known range and given set of moments. Such bounds can be useful in ordering of random variables in terms of risk and in PERT analysis where there is only incomplete stochastic information concerning the variables under investigation. Explicit closed form solutions are also given involving alpha-unimodal random variables having a known mean for two particularly important measures of risk—the squared distance or variance, and the absolute deviation. In addition, optimal tight bounds are given for the probability of ruin in the collective risk model when the severity distribution has an alpha-unimodal distribution with known moments.

Pareto-Optimal Reinsurance Based on TVaR Premium Principle and Vajda Condition

Reinsurance is an effective risk management tool for insurers to stabilize their profitability. In a typical reinsurance treaty, an insurer cedes part of the loss to a reinsurer. As the insurer faces an increasing number of total losses in the insurance market, the insurer might expect the reinsurer to bear an increasing proportion of the total loss, that is the insurer might expect the reinsurer to pay an increasing proportion of the total claim amount when he faces an increasing number of total claims in the insurance market. Motivated by this, we study the optimal reinsurance problem under the Vajda condition. To prevent moral hazard and reflect the spirit of reinsurance, we assume that the retained loss function is increasing and the ceded loss function satisfies the Vajda condition. We derive the explicit expression of the optimal reinsurance under the TVaR risk measure and TVaR premium principle from the perspective of both an insurer and a reinsurer. Our results show that the explicit expression of the optimal reinsurance is in the form of two or three interconnected line segments. Under an additional mild constraint, we get the optimal parameters and find the optimal reinsurance strategy is full reinsurance, no reinsurance, stop loss reinsurance, or quota-share reinsurance. Finally, we gave an example to analyze the impact of the weighting factor on optimal reinsurance.

Exponential martingale for compound Poisson process with latent variable and its applications

In this article, we construct an exponential martingale for the compound Poisson process with latent variable. With the help of this exponential martingale, we provide an asymptotic behavior of the coherent entropic risk measure for the compound Poisson process and a deviation inequality for the ruin probability of the partly shifted risk process.

Stressed portfolio optimization with semiparametric method

Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks,while the traditional mean–variance approach may fail to perform well.This study proposes an innovative semiparametric method consisting of two modeling components:the nonparametric estimation and copula method for each marginal distribution of the portfolio and their joint distribution,respectively.We then focus on the optimal weights of the stressed portfolio and its optimal scale beyond the Gaussian restriction.Empirical studies include statistical estimation for the semiparametric method,risk measure minimization for optimal weights,and value measure maximization for the optimal scale to enlarge the investment.From the outputs of short-term and long-term data analysis,optimal stressed portfolios demonstrate the advantages of model flexibility to account for tail risk over the traditional mean–variance method.

OPTIMAL REINSURANCE UNDER EXPECTED VALUE PRINCIPLE

The paper concerns the problem how to purchase the reinsurance in order to make the insurer and the reinsurance company＇s total risk to be least under the expected value principle. When the insurer and reinsurance company take arbitrary risk measures, sufficient con- ditions for optimality of reinsurance contract are given within the restricted class of admissible contracts. Further, the explicit forms of optimal reinsurance contract under several special risk measures are given, and the method to decide parameters as well.

A New Risk Measure MMVaR:Properties and Empirical Research

The paper presents the properties of an alternative method,which measures market risk over time-horizon exceeding one day:Mark to market value at risk(MMVaR).Relying on the minimal returns during the time interval,this method not only considers the non-normality of data and information about sample size,but also meets the requirement of increasing the minimal capital ratio in BaselⅢ,basically.The authors theoretically prove the translation invariance,monotonicity and subadditivity of MMVaR as a risk measure under some conditions,and study its finite sample properties through Monte Carlo simulations.The empirical analysis shows that MMVaR can measure multi-period risk accurately.

Mean-field BSDEs with jumps and dual representation for global risk measures

We study mean-field BSDEs with jumps and a generalized mean-field operator that can capture higher-order interactions.We interpret the BSDE solution as a dynamic risk measure for a representative bank whose risk attitude is influenced by the system.This influence can come in a wide class of choices,including the average system state or average intensity of system interactions.Using Fenchel−Legendre transforms,our main result is a dual representation for the expectation of the risk measure in the convex case.In particular,we exhibit its dependence on the mean-field operator.

A Worst-Case Risk Measure by G-VaR

G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,and can be applied to large portfolios of several hundred dimensions with low computational cost.We also apply G-VaR to robust portfolio optimization,thereby providing a tractable means to facilitate optimal allocations under the condition of market ambiguity.

First and Second Order Asymptotics of the Spectral Risk Measure for Portfolio Loss Under Multivariate Regular Variation

In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-order asymptotics of the spectral risk measure of portfolio loss is also presented.In order to illustrate the derived results,a numerical example with Monte Carlo simulation is carried out.

The Maximum Principle for One Kind of Stochastic Optimization Problem and Application in Dynamic Measure of Risk

The authors get a maximum principle for one kind of stochastic optimization problem motivated by dynamic measure of risk. The dynamic measure of risk to an investor in a financial market can be studied in our framework where the wealth equation may have nonlinear coefficients.

Time Consistent Multi-period Worst-Case Risk Measure in Robust Portfolio Selection

In this paper,we first construct a time consistent multi-period worst-case risk measure,which measures the dynamic investment risk period-wise from a distributionally robust perspective.Under the usually adopted uncertainty set,we derive the explicit optimal investment strategy for the multi-period robust portfolio selection problem under the multi-period worst-case risk measure.Empirical results demonstrate that the portfolio selection model under the proposed risk measure is a good complement to existing multi-period robust portfolio selection models using the adjustable robust approach.