On occupation times in the red of Lévy risk models

In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level 0) up to an (independent) exponential horizon for spectrally negative Lévy risk processes and refracted spectrally negative Lévy risk processes. This result improves the existing literature in which only the Laplace transforms are known. Due to the close connection between occupation time and many other quantities, we provide a few applications of our results including future drawdown, inverse occupation time, Parisian ruin with exponential delay, and the last time at running maximum.     

The Tax Identity For Markov Additive Risk Processes

Taxed risk processes, i.e. processes which change their drift when reaching new maxima, represent a certain type of generalizations of Lévy and of Markov additive processes (MAP), since the times at which their Markovian mechanism changes are allowed to depend on the current position. In this paper we study generalizations of the tax identity of Albrecher and Hipp (2007) from the classical risk model to more general risk processes driven by spectrally-negative MAPs. We use the Sparre Andersen risk processes with phase-type interarrivals to illustrate the ideas in their simplest form.     

Coupling and option price comparisons in a jump-diffusion model

In this paper, we examine the dependence of option prices in a general jump-diffusion model on the choice of martingale pricing measure. Since the model is incomplete, there are many equivalent martingale measures. Each of these measures corresponds to a choice for the market price of diffusion risk and the market price of jump risk. Our main result is to show that for convex payoffs, the option price is increasing in the jump-risk parameter. We apply this result to deduce general inequalities, comparing the prices of contingent claims under various martingale measures, which have been proposed in the literature as candidate pricing measures.

Our proofs are based on couplings of stochastic processes. If there is only one possible jump size then we are able to utilize a second coupling to extend our results to include stochastic jump intensities.     

基于模糊RBF神经网络的单位廉政风险评价研究

廉政风险防控是反腐败工作的新举措,对风险的评价是风险管理中一个不可缺少的流程.首先运用文献研究方法,提出廉政风险评价的初步指标,再运用帕累托理论得到经过约减的指标体系.建立基于模糊RBF神经网络的廉政风险水平评价模型.并在某军区对20个单位的廉政风险水平进行评价,与传统的评价模型相比,模型能够克服评估过程中的随机性和不确定性,以及计算过程中容易陷入局部极小的问题.     

Strong Law of Large Numbers and Central Limit Theorems for Functionals of Inhomogeneous Semi-Markov Processes

Limit theorems for functionals of classical (homogeneous) Markov renewal and semi-Markov processes have been known for a long time, since the pioneering work of Pyke Schaufele (Limit theorems for Markov renewal processes, Ann. Math. Statist., 35(4):1746–1764, 1964). Since then, these processes, as well as their time-inhomogeneous generalizations, have found many applications, for example, in finance and insurance. Unfortunately, no limit theorems have been obtained for functionals of inhomogeneous Markov renewal and semi-Markov processes as of today, to the best of the authors’ knowledge. In this article, we provide strong law of large numbers and central limit theorem results for such processes. In particular, we make an important connection of our results with the theory of ergodicity of inhomogeneous Markov chains. Finally, we provide an application to risk processes used in insurance by considering a inhomogeneous semi-Markov version of the well-known continuous-time Markov chain model, widely used in the literature.     

Tail risk measures and risk allocation for the class of multivariate normal mean–variance mixture distributions

The Conditional Tail Expectation (CTE), also known as the Expected Shortfall and Tail-VaR, has received much attention as a preferred risk measure in finance and insurance applications. A related risk management exercise is to allocate the amount of the CTE computed for the aggregate or portfolio risk into individual risk units, a procedure known as the CTE allocation. In this paper we derive analytic formulas of the CTE and its allocation for the class of multivariate normal mean–variance mixture (NMVM) distributions, which is known to be extremely flexible and contains many well-known special cases as its members. We also develop the closed-form expression of the conditional tail variance (CTV) for the NMVM class, an alternative risk measure proposed in the literature to supplement the CTE by capturing the tail variability of the underlying distribution. To illustrate our findings, we focus on the multivariate Generalized Hyperbolic Distribution (GHD) family which is a popular subclass of the NMVM in connection with Lévy processes and contains some common distributions for financial modelling. In addition, we also consider the multivariate slash distribution which is not a member of GHD family but still belongs to the NMVM class. Our result is an extension of the recent contribution of Ignatieva and Landsman (2015).     

Fuzzy linear programming models for new product design using QFD with FMEA

Quality function deployment (QFD) is a customer-driven approach in processing new product developments in order to maximize customer satisfaction. Determining the fulfillment levels of design requirements (DRs) and parts characteristics (PCs) is an important decision problem during QFD activity processes for new product development. Unlike the existing literature, which mainly focuses on the determination of DRs, this paper proposes fuzzy linear programming models to determine the fulfillment levels of PCs under the requirement to achieve the determined contribution levels of DRs for customer satisfaction. In addition, considering the design risk, this paper incorporates failure modes and effect analysis (FMEA) into QFD processes, which is treated as the constraint in the models. To cope with the vague nature of product development processes, fuzzy approaches are used for both FMEA and QFD. The illustration of the proposed models is performed with a numerical example to demonstrate the applicability in practice.     

A Continuous-Risk Decision Analysis of Total Hip Replacement

Stochastic trees are stochastic processes, such as continuous-time Markov chains, which may be represented using tree diagrams. Continuous-risk utility assessment is a methodology that differs from standard assessment protocols by offering choices between alternatives which are not ‘sure’ things, thus enabling more realistic and familiar assessment scenarios to be posed. In this paper we develop, using information from the medical literature, stochastic tree models of the total hip replacement decision alternatives facing a patient with advanced osteoarthritis of the hip. We describe a decision analytic approach to the problem which uses continuous-risk utility assessment, and present empirical assessment results. We explore the sensitivity of the subjects' treatment recommendations to changes in model parameters and elicited preference values, offering insights into the variety of patient risk attitudes and preferences about functional well-being and the robustness of the total hip replacement decision to them.     

First-order optimization algorithms via inertial systems with Hessian driven damping

For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main feature is that they measure risk of processes that are functions of the history of a base process. We introduce a new concept of conditional stochastic time consistency and we derive the structure of process-based risk measures enjoying this property. We show that they can be equivalently represented by a collection of static law-invariant risk measures on the space of functions of the state of the base process. We apply this result to controlled Markov processes and we derive dynamic programming equations. We also derive dynamic programming equations for multistage stochastic programming with decision-dependent distributions.

     

A tensorial framework for strain induced damage of plastically deformed metals

A tensorial framework for strain induced ductile damage of plastically deformed metals is developed in terms of both plastic flow theory and continuum damage mechanics. A symmetric second order damage rate tensor is used in order to study various processes with large finite deformations in combination with damage analysis. The definition of this tensor is physically meaningful since its volumetric and deviatoric parts describe the damage increments caused by an increase in the void volume and by a change in the shape of the void, respectively. Such a view on damage kinetics leads to the introduction of two measures for damage assessment which allow predicting not only a risk of macroscopic failure but also the onset of void coalescence. Material functions appearing in the constitutive equations for damage are determined both by own experiments and by known results from literature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ruin Probabilities in Cox Risk Models with Two Dependent Classes of Business

In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Markovian intensity. Under this assumption, we not only study the sum of the two individual risk processes but also investigate the two-dimensional risk process formed by considering the two individual processes separately. For each of the two risk processes we derive an expression for the ruin probability, and then construct an upper bound for the ruin probability. We next assume that the intensity of the two claim-number processes follows a Markov chain. In this case, we examine the ruin probability of the sum of the two individual risk processes. Specifically, a differential system for the ruin probability is derived and numerical results are obtained for exponential claim sizes.     

The influence of non-linear dependencies on the basis risk of industry loss warranties

Index-linked catastrophic loss instruments represent an alternative to traditional reinsurance to hedge against catastrophic losses. The use of these instruments comes with benefits, such as a reduction of moral hazard and higher transparency. However, at the same time, it introduces basis risk as a crucial key risk factor, since the index and the company’s losses are usually not fully dependent. The aim of this paper is to examine the impact of basis risk on an insurer’s solvency situation when an industry loss warranty contract is used for hedging. Since previous literature has consistently stressed the importance of a high degree of dependence between the company’s losses and the industry index, we extend previous studies by allowing for non-linear dependencies between relevant processes (high-risk and low-risk assets, insurance company’s loss and industry index). The analysis shows that both the type and degree of dependence play a considerable role with regard to basis risk and solvency capital requirements and that other factors, such as relevant contract parameters of index-linked catastrophic loss instruments, should not be neglected to obtain a comprehensive and holistic view of their effect upon risk reduction.     

Stochastic optimization algorithms for barrier dividend strategies

This work focuses on finding optimal barrier policy for an insurance risk model when the dividends are paid to the share holders according to a barrier strategy. A new approach based on stochastic optimization methods is developed. Compared with the existing results in the literature, more general surplus processes are considered. Precise models of the surplus need not be known; only noise-corrupted observations of the dividends are used. Using barrier-type strategies, a class of stochastic optimization algorithms are developed. Convergence of the algorithm is analyzed; rate of convergence is also provided. Numerical results are reported to demonstrate the performance of the algorithm.     

Stable convergence of semimartingales

Under a nesting condition on the sequence of histories, stable weak convergence of semimartingales to processes with conditionally independent increments is considered. Apart from ensuring the stability property, the nesting condition is more natural in some applications than an alternative measurability condition which appears in the literature.     

Concentration measures in risk management

Following the increasing use of external and internal credit ratings made by the Bank regulation, credit risk concentration has become one of the leading topics in modern finance. In order to measure separately single-name and sectoral concentration risk, the literature proposes specific concentration indexes and models, which we review in this paper. Following the guideline proposed by Basel 2 on risk integration, we believe that standard approaches could be improved by studying a new measure of risk that integrates single-name and sectoral credit risk concentration in a coherent way. The main objective of this paper is to propose a novel index useful to measure credit risk concentration integrating single-name and sectoral components. From a theoretical point of view, our measure of risk shows interesting mathematical properties; empirical evidences are given on the basis of a data set. Finally, we have compared the results achieved following our proposal with respect to the common procedures proposed in the literature.     

The semi-Markov beta-Stacy process: a Bayesian non-parametric prior for semi-Markov processes.

The literature on Bayesian methods for the analysis of discrete-time semi-Markov processes is sparse. In this paper, we introduce the semi-Markov beta-Stacy process, a stochastic process useful for the Bayesian non-parametric analysis of semi-Markov processes. The semi-Markov beta-Stacy process is conjugate with respect to data generated by a semi-Markov process, a property which makes it easy to obtain probabilistic forecasts. Its predictive distributions are characterized by a reinforced random walk on a system of urns.

     

Red Blood Cell Transfusion Safety: Probabilistic Risk Assessment and Cost/ Benefits of Risk Reduction Strategies

While transfusion safety, particularly with respect to transfusion-transmitted infectious diseases, has improved dramatically over the past several decades, progress in other clinical processes of blood product transfusion continue with highly variable practices and human errors that contribute to adverse outcomes. In this paper, we study the adverse outcome risk in red blood cell (RBC) transfusion in the United States using Probabilistic Risk Assessment (PRA). PRA allows us to map, in a comprehensive manner, the various types of events that may contribute to an adverse outcome, including socio-technical factors such as the risk coming from human error; and allows us to formalize the logical relationships among those events and the adverse outcome risk. We utilize the PRA model to assess the risk to the patient from RBC transfusion in the United States, to identify the major risk points in the transfusion process, and to evaluate the costs and benefits of several risk reduction strategies. Our data come from published studies in the medical literature. We find that the risk of a potentially severe outcome (e.g., mortality, major injury or other serious long-term consequences, a life threatening incident) from RBC transfusion lies in the interval [10.4327,511.2] per 100,000 units of RBC transfused, with a point estimate of 25.4527. The leading causes of severe outcomes include circulatory overload and bacterial infection. Acute hemolytic reactions, which are mainly caused by erroneous administration of the blood, also contribute significantly to severe outcomes of transfusion. Interestingly, our analysis indicates that an intervention that is targeted at reducing the risk of the erroneous administration of blood (through training programs or technology investments) has a higher potential impact in reducing the severe outcome risk from RBC transfusion than additional screening to further reduce the risk of transfusion-transmitted viral infections, of HIV 1-2, hepatitis B, and hepatitis C, which the lay public fears most. Furthermore, such an error reduction program will be more cost-effective than the additional screening of donated blood. Our study provides guidelines for public policy to improve the safety of RBC transfusion in the United States.