The surplus prior to ruin and the deficit at ruin for a correlated risk process

This paper presents an explicit characterization for the joint probability density function of the surplus immediately prior to ruin and the deficit at ruin for a general risk process, which includes the Sparre-Andersen risk model with phase-type inter-claim times and claim sizes. The model can also accommodate a Markovian arrival process which enables claim sizes to be correlated with the inter-claim times. The marginal density function of the surplus immediately prior to ruin is specifically considered. Several numerical examples are presented to illustrate the application of this result.     

Stationarity and the start of a renewal process

Abstract

In his short article Professor Seal considers inter alia the suitability of the renewal approach to the occurrence scheme in risk theory. He gives a catalog of four facts which according to him make the renewal approach less reasonable. About the two first facts he himself says that they may be removed as more actual experience becomes available so I will not discuss them but consider the two last only     

Probability of ruin for a risk process with claims cost inflation

Abstract

This paper has been inspired by a very interesting article by Taylor (1979) in which he considered the effect of claims cost inflation on a compound Poisson risk process. The present paper divides naturally into two parts. In the first part we show, under very general conditions, that if claims costs are increasing and if the premiums are increasing at the same rate then ultimate ruin is certain for the risk process. In the second part we try to determine how fast the premiums should increase in order that ultimate ruin should not be certain for such a risk process.     

A diffusion approximation for the ruin function of a risk process with compounding assets

Abstract

The traditional theory of collective risk is concerned with fluctuations in the capital reserve {Y(t): t ?O} of an insurance company. The classical model represents {Y(t)} as a positive constant x (initial capital) plus a deterministic linear function (cumulative income) minus a compound Poisson process (cumulative claims). The central problem is to determine the ruin probability ψ(x) that capital ever falls to zero. It is known that, under reasonable assumptions, one can approximate {Y(t)} by an appropriate Wiener process and hence ψ(.) by the corresponding exponential function of (Brownian) first passage probabilities. This paper considers the classical model modified by the assumption that interest is earned continuously on current capital at rate β > O. It is argued that Y(t) can in this case be approximated by a diffusion process Y*(t) which is closely related to the classical Ornstein-Uhlenbeck process. The diffusion {Y*(t)}, which we call compounding Brownian motion, reduces to the ordinary Wiener process when β = O. The first passage probabilities for Y*(t) are found to form a truncated normal distribution, which approximates the ruin function ψ(.) for the model with compounding assets. The approximate expression for ψ(.) is compared against the exact expression for a special case in which the latter is known. Assuming parameter values for which one would anticipate a good approximation, the two expressions are found to agree extremely well over a wide range of initial asset levels.     

On a risk measure inspired from the ruin probability and the expected deficit at ruin

In this paper, we study a risk measure derived from ruin theory defined as the amount of capital needed to cope in expectation with the first occurrence of a ruin event. Specifically, within the compound Poisson model, we investigate some properties of this risk measure with respect to the stochastic ordering of claim severities. Particular situations where combining risks yield diversification benefits are identified. Closed form expressions and upper bounds are also provided for certain claim severities.     

最佳风险管理及其标准可加快银行成长进程

风险管理是商业银行经营活动中的一个永恒的话题,承担和管理风险是商业银行的基本职责,也是商业银行业务不断创新发展的动力源泉之一。商业银行如何有效防范与化解经营过程中面临的各种风险,已成为影响银行发展的关键因素之一。业界普遍认为,风险管理对商业银行的经营有如下作用：风险管理能够成为商业银行实施经营战略的手段,极大地改变了商业银行的经营管理模式;     

Some properties of the ruin function in the collective theory of risk

Abstract

It is well known that the chief aim of all theory of risk is to attain a sort of objective and somehow confirmed opinion of how and to which extent an insurance company ought to reinsure its risks in order that the probability of ruin by random fluctuations of the risk process shall become so small that it can be overlooked in practice.     

Analysis of ruin measures for the classical compound Poisson risk model with dependence

In this paper, we consider an extension to the classical compound Poisson risk model. Historically, it has been assumed that the claim amounts and claim inter-arrival times are independent. In this contribution, a dependence structure between the claim amount and the interclaim time is introduced through a Farlie–Gumbel–Morgenstern copula. In this framework, we derive the integro-differential equation and the Laplace transform (LT) of the Gerber–Shiu discounted penalty function. An explicit expression for the LT of the discounted value of a general function of the deficit at ruin is obtained for claim amounts having an exponential distribution.     

Asymptotics of ruin probabilities for controlled risk processes in the small claims case

We consider a risk process with the possibility of investment into a risky asset. The aim of the paper is to obtain the asymptotic behaviour of the ruin probability under the optimal investment strategy in the small claims case. In addition we prove convergence of the optimal investment level as the initial capital tends to infinity.     

On the probability of ruin in the collective risk theory for insurance enterprises with oly negative risk sums

Abstract

1. The determination of the probability that an insurance company once in the future will be brought to ruin is a problem of great interest in insurance mathematics. If we know this probability, it does not only give us a possibility to estimate the stability of the insurance company, but we may also decide which precautions, in the form of f. ex. reinsurance and loading of the premiums, should be taken in order to make the probability of ruin so small that in practice no ruin is to be feared.     

On the discounted aggregate claim costs until ruin in dependent Sparre Andersen risk processes

In this paper, a dependent Sparre Andersen risk process in which the joint density of the interclaim time and the resulting claim severity satisfies the factorization as in Willmot and Woo is considered. We study a generalization of the Gerber–Shiu function (i) whose penalty function further depends on the surplus level immediately after the second last claim before ruin; and (ii) which involves the moments of the discounted aggregate claim costs until ruin. The generalized discounted density with a moment-based component proposed in Cheung plays a key role in deriving recursive defective renewal equations. We pay special attention to the case where the marginal distribution of the interclaim times is Coxian, and the required components in the recursion are obtained. A reverse type of dependency structure, where the claim severities follow a combination of exponentials, is also briefly discussed, and this leads to a nice explicit expression for the expected discounted aggregate claims until ruin. Our results are applied to generate some numerical examples involving (i) the covariance of the time of ruin and the discounted aggregate claims until ruin; and (ii) the expectation, variance and third central moment of the discounted aggregate claims until ruin.     

Pricing and managing risks of ruin contingent life annuities under regime switching variance gamma process

We propose a model for valuing ruin contingent life annuities under the regime-switching variance gamma process. The Esscher transform is employed to determine the equivalent martingale measure. The PIDE approach is adopted for the pricing formulation. Due to the path dependency of the payoff of the insurance product and the non-existence of a closed-form solution for the PIDE, the finite difference method is utilized to numerically calculate the value of the product. To highlight some practical features of the product, we present a numerical example. Finally, we examine numerically the performance of a simple hedging strategy by investigating the terminal distribution of hedging errors and the associated risk measures such as the value at risk and the expected shortfall. The impacts of the frequency of re-balancing the hedging portfolio on the quality of hedging are also discussed.     

Asymptotic ruin probabilities for a discrete-time risk model with dependent insurance and financial risks

This contribution focuses on a discrete-time risk model in which both insurance risk and financial risk are taken into account and they are equipped with a wide type of dependence structure. We derive precise asymptotic formulas for the ruin probabilities when the insurance risk has a dominatedly varying tail. In the special case of regular variation, the corresponding formula is proved to be uniform for the time horizon.     

Fear and risk in the audit process

Relying on an ethnographic study conducted in the French branch of a big audit firm and using a psychodynamic perspective to interpret the collected data, we show that auditors’ sense of comfort (Pentland, 1993) arises only at the end of the audit process, and that the rest of the time, public accountants are inhabited primarily by fear. Fear plays a crucial but ambivalent role in auditing. On one hand, auditors and audit firms cultivate this feeling through informal and formal techniques to stimulate vigilance, encourage self-surpassment, mitigate the anesthetizing effect of habit and maintain reputation. On the other hand, audit teams’ members strive to alleviate their fear in order to form and convey their conclusions with a certain degree of comfort. In the field, driven by fear, they manage to finally become comfortable either by mobilizing their ‘practical intelligence’ (an intelligence of the body which helps them handle that which, in their mission, cannot be obtained through the strict execution of standardized procedures) or by adopting defensive strategies (such as distancing themselves from work-related problems, mechanically applying audit methodologies or relaxing their conception of a job well done). Fear and risk are closely related phenomena. Michael Power (2007a, p. 180) notes that ‘the significant driver of the managerialization of risk management is an institutional fear and anxiety’. Yet the experience of fear and the role that fear plays in risk management processes is most often overlooked in the literature. In this respect, our study contributes to ‘emotionalize’ and challenge the cognitive and technical orientation adopted by most academics and regulators in their understanding of audit risks and auditors’ scepticism. We also discuss a number of avenues for future research with a view to encouraging further examination of the role that emotions play in the audit process.     

融资约束、股权结构和股利平稳性

稳定的分红对现金流要求较高,融资约束的存在可能会加剧企业对内部现金流的依赖,影响现金股利的发放。不同股权结构下代理成本差异很大,现金股利分配可以通过减少自由现金流来降低代理成本,因此股权结构对融资约束与股利平稳性关系的调节作用值得研究。从代理成本的视角,以我国2012—2016年A股上市公司数据为研究对象,对融资约束、股权结构和股利平稳性之间的关系进行了理论分析与实证检验。研究结果表明,融资约束抑制了股利平稳性,股权结构在二者之间的关系中起到了调节作用,具体表现为,国有控股、较高的股权集中度和股权制衡度均能够削弱融资约束对股利平稳性的负向影响。因此,加强上市公司股权结构的治理以及解决企业当前的融资困境对促进现金股利的平稳性尤为重要。     

Convolution of uniform distributions and ruin probability

Abstract

This paper presents an “operational calculus” method for evaluating the convolution of uniform distributions and applies it to solve a problem in ruin theory.     

Keynesian and monetarist theories of the monetary transmission process: Doctrinal aspects

This paper investigates the doctrinal link underlying differences between Keynesian and monetarist approaches regarding the transmission mechanism of monetary policy. Consideration of the post-General Theory literature reveals that a key aspect of that link concerns the velocity of circulation of money. The Keynesian emphasis on compartmentalizing the demand for money into active and idle components resulted in a mechanical interpretation of velocity and the associated view that money does not matter. The monetarist tradition illustrates the behavioral perspective adduced to velocity via adaptive price expectations by earlier quantity theorists leading to a capital-theoretic reformulation of the quantity theory in terms of a stable demand function for money.     

Friction in the trading process and the estimation of systematic risk

This paper considers how estimates of the market model beta parameter can be biased by friction in the trading process (information, decision, and transaction costs) that (a) leads to a distinction between observed and ‘true’ returns; (b) causes observed returns to be generated asynchronously for a set of interdependent securities; and (c) thereby introduces serial cross-correlation into security returns. Several propositions are derived from which consistent estimators of beta are obtained, and the effect of differencing interval length on beta estimates is specified. The formulation is contrasted with the related analyses of Scholes-Williams (1977) and Dimson (1979).