Absolute Ruin Probabilities in a Jump Diffusion Risk Model with Investment

Abstract

This article considers the compound Poisson insurance risk model perturbed by diffusion with investment. We assume that the insurance company can invest its surplus in both a risky asset and the risk-free asset according to a fixed proportion. If the surplus is negative, a constant debit interest rate is applied. The absolute ruin probability function satisfies a certain integro-differential equation. In various special cases, closed-form solutions are obtained, and numerical illustrations are provided.     

On the Gerber-Shiu Discounted Penalty Function for the Ordinary Renewal Risk Model with Constant Interest

Abstract

In this paper we study the Gerber-Shiu discounted penalty function for the ordinary renewal risk model modified by the constant interest on the surplus. Explicit answers are expressed by an infinite series, and a relational formula for some important joint density functions is derived. Applications of the results to the compound Poisson model are given. Finally, a lower bound and an upper bound for the ultimate ruin probability are derived.     

Approximation methods for multiple period Value at Risk and Expected Shortfall prediction

In this paper, we are interested in predicting multiple period Value at Risk and Expected Shortfall based on the so-called iterating approach. In general, the properties of the conditional distribution of multiple period returns do not follow easily from the one-period data generating process, rendering this a non-trivial task. We outline a framework that forms the basis for setting approximations and study four different approaches. Their performance is evaluated by means of extensive Monte Carlo simulations based on an asymmetric GARCH model, implying conditional skewness and excess kurtosis in the multiple period returns. This simulation-based approach was the best one, closely followed by that of assuming a skewed t-distribution for the multiple period returns. The approach based on a Gram–Charlier expansion was not able to cope with the implied non-normality, while the so-called Root-k approach performed poorly. In addition, we outline how the delta-method may be used to quantify the estimation error in the predictors and in the Monte Carlo study we found that it performed well. In an empirical illustration, we computed 10-day Value at Risk’s and Expected Shortfall for Brent Crude Oil, the EUR/USD exchange rate and the S&P 500 index. The Root-k approach clearly performed the worst and the other approaches performed quite similarly, with the simulation based approach and the one based on the skewed t-distribution somewhat better than the one based on the Gram–Charlier expansion.     

Optimal Reinsurance and Investment for a Jump Diffusion Risk Process under the CEV Model

Abstract

We consider an optimal reinsurance-investment problem of an insurer whose surplus process follows a jump-diffusion model. In our model the insurer transfers part of the risk due to insurance claims via a proportional reinsurance and invests the surplus in a “simplified” financial market consisting of a risk-free asset and a risky asset. The dynamics of the risky asset are governed by a constant elasticity of variance model to incorporate conditional heteroscedasticity. The objective of the insurer is to choose an optimal reinsurance-investment strategy so as to maximize the expected exponential utility of terminal wealth. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Explicit forms for the optimal reinsuranceinvestment strategy and the corresponding value function are obtained. Numerical examples are provided to illustrate how the optimal investment-reinsurance policy changes when the model parameters vary.     

Moments of Discounted Dividends for a Threshold Strategy in the Compound Poisson Risk Model

Abstract

We consider a compound Poisson risk model in which part of the premium is paid to the shareholders as dividends when the surplus exceeds a specified threshold level. In this model we are interested in computing the moments of the total discounted dividends paid until ruin occurs. However, instead of employing the traditional argument, which involves conditioning on the time and amount of the first claim, we provide an alternative probabilistic approach that makes use of the (defective) joint probability density function of the time of ruin and the deficit at ruin in a classical model without a threshold. We arrive at a general formula that allows us to evaluate the moments of the total discounted dividends recursively in terms of the lower-order moments. Assuming the claim size distribution is exponential or, more generally, a finite shape and scale mixture of Erlangs, we are able to solve for all necessary components in the general recursive formula. In addition to determining the optimal threshold level to maximize the expected value of discounted dividends, we also consider finding the optimal threshold level that minimizes the coefficient of variation of discounted dividends. We present several numerical examples that illustrate the effects of the choice of optimality criterion on quantities such as the ruin probability.     

The Ruin Probability of a Discrete Time Risk Model under Constant Interest Rate with Heavy Tails

This paper investigates the ultimate ruin probability of a discrete time risk model with a positive constant interest rate. Under the assumption that the gross loss of the company within one year is subexponentially distributed, a simple asymptotic relation for the ruin probability is derived and compared to existing results.     

Simulating Ruin Probabilities for a Class of Semimartingales by Importance Sampling Methods

We consider the problem of finding the probability of ruin when the risk process is assumed to be a special semimartingale with absolutely continuous characteristics. We show how the generalized Girsanov theorem can be used in connection with Monte Carlo simulation to obtain estimates of the ruin probabilities. It is shown by both analytical and numerical examples that these methods can be significantly better than ordinary simulations provided the new measure is chosen with some care.     

Asymptotic Theory for a Risk Process with a High Dividend Barrier

The only way to avoid ruin in the classical model of the collective risk theory is that the surplus increases to infinity. We consider a modified model with a dividend barrier that prevents this behavior. It is shown that there is a simple approximation formula for the time of ruin when the level of the dividend barrier is high and the Cramér-Lundberg condition is satisfied. A numerical example is presented in the case when the claims are exponentially distributed. The relation to queuing theory is used to derive the proportion of time the surplus is below some given level.     

Ruin probability at a given time for a model with liabilities of the fractional Brownian motion type: A partial differential equation approach

In this paper we study the ruin probability at a given time for liabilities of diffusion type, driven by fractional Brownian motion with Hurst exponent in the range (0.5, 1). Using fractional Itô calculus we derive a partial differential equation the solution of which provides the ruin probability. An analytical solution is found for this equation and the results obtained by this approach are compared with the results obtained by Monte-Carlo simulation.     

The Valuation of Options When Asset Returns Are Generated by a Binomial Process

This paper values options on assets whose returns, over a finite interval of time, are generated by a binomial process. It shows that a simple valuation relationship, between the option and the underlying stock, obtains if investors have preference functions that belong to a particular class, even if opportunities to hedge do not exist. One particular application of the theory is in the case where the stock price over a finite interval could increase by an amount, fall by the same amount, or stay at the same level. The results in this paper may be viewed as the foundation of the preference-based approaches to obtaining a risk neutral valuation relationship.     

我国商业银行中小企业信贷风险评估体系的构建

开展中小企业贷款业务是商业银行优化信贷资产结构的重要措施，快速、准确评估其信贷风险是商业银行亟须解决的技术问题。经过长期实地调研，本文建立了适用于我国的中小企业信贷风险评估体系，其中，所建非财务指标体系，从行业环境、企业经营管理水平、经营者经验与素质、信用品质四方面进行评估；财务指标体系包括现金流流动负债比、净资产总资产比、息税前利润流动负债比、总资产周转速度、流动比率、现金流贷款比六个指标。以Logit统计回归模型为基础建立的评估模型，在分别评估非财务指标信息和财务指标信息后，加权相加两方面结果得到综合评估结果。实证检验证明，该评估体系的评估正确率达到95％以上。     

我国商业银行中小企业信贷风险评估体系的构建

开展中小企业贷款业务是商业银行优化信贷资产结构的重要措施,快速、准确评估其信贷风险是商业银行亟须解决的技术问题.经过长期实地调研,本文建立了适用于我国的中小企业信贷风险评估体系,其中,所建非财务指标体系,从行业环境、企业经营管理水平、经营者经验与素质、信用品质四方面进行评估;财务指标体系包括现金流流动负债比、净资产总资产比、息税前利润流动负债比、总资产周转速度、流动比率、现金流贷款比六个指标.以Logit统计回归模型为基础建立的评估模型,在分别评估非财务指标信息和财务指标信息后,加权相加两方面结果得到综合评估结果.实证检验证明,该评估体系的评估正确率达到95%以上.     

The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds

Abstract:  Current research suggests that the large downside risk in hedge fund returns disqualifies the variance as an appropriate risk measure. For example, one can easily construct portfolios with nonlinear pay-offs that have both a high Sharpe ratio and a high downside risk. This paper examines the consequences of shortfall-based risk measures in the context of portfolio optimization. In contrast to popular belief, we show that negative skewness for optimal mean-shortfall portfolios can be much greater than for mean-variance portfolios. Using empirical hedge fund return data we show that the optimal mean-shortfall portfolio substantially reduces the probability of small shortfalls at the expense of an increased extreme crash probability. We explain this by proving analytically under what conditions short-put payoffs are optimal for a mean-shortfall investor. Finally, we show that quadratic shortfall or semivariance is less prone to these problems. This suggests that the precise choice of the downside risk measure is highly relevant for optimal portfolio construction under loss averse preferences.     

Reducing Regulatory Risk: The Case for a New Regulatory Contract with the Privatized Utilities

Privatization was intended to reverse the inefficiencies of state ownership. When the public utilities were privatized in the UK, between 1984 and 1996, newdedicated regulatory offices were established: Oftel, Ofgas, Ofwat, Offer and the ORR. Terms of reference for the regulators were set out in the privatization legislation, but more generally the regulators were given considerable discretion over their industries. Against the background of the Government Green Paper on the future of regulation in the UK, this article argues that while regulatory discretion was desirable in the early days of regulation, there is now a stronger case for introducing 'contracts' which constrain regulatory discretion and reduce regulatory risk.     

公司为股东担保的合同效力与银行法律风险

30个汉字与2700亿元银行资产
　　公司为股东担保,并不是一个新鲜的话题。“董事、经理不得以公司资产为本公司的股东或者其他个人债务提供担保”。这样的表述,早在1993年《公司法》颁布时,第六十条第三款就已经写明,只是当时并没有引起太大的关注。直到2000年,最高人民法院出台《关于适用〈担保法〉若干问题的解释》,第四条明确指出：“董事、经理违反《公司法》第六十条的规定,以公司资产为本公司的股东或者其他个人债务提供担保的,担保合同无效”,才令人吃惊;而且,最高人民法院在2001年中国工商银行诉中福实业公司借款担保纠纷一案,把这一条款进一步演化成现实的案例后,就对债权人、尤其是商业银行业界产生了巨大的冲击。     

The Effect of Errors in Variables on Tests for a Risk Premium in Forward Exchange Rates

Conventional tests for a risk premium in the price of forward exchange use the subsequently realized spot rate as a proxy for prior expectations. Use of this proxy creates a serious errors-in-variables problem which makes it difficult to reject the null hypothesis of zero risk premium. Use of a better proxy for expectations indicates the presence of a risk premium in the forward exchange rate of all countries analyzed.     

The Consequences for a Monopolistic Insurance Firm of Evaluating Risk Better than Customers: The Adverse Selection Hypothesis Reversed

This article models a situation in which a monopolistic insurer evaluates risk better than its customers. The resulting equilibrium allocations are compared to the consequences of the standard adverse selection hypothesis. On the positive side, they exhibit the property that low-risk people are better covered than higher-risk people. On the normative side, the article shows that there are two reasons for avoiding excessive risk classification: one is the classical destruction of insurance possibilities, and the other comes from the distrustful atmosphere generated by new asymmetric information.     

同心协力 加快评估立法进程——在全国人大财经委资产评估法起草组成立暨第一次会议上的讲话

今天是我国评估行业发展史上一个非常重要的日子。评估行业经过近20年的发展,在全国人大常委会领导的关心支持下,资产评估法得以正式启动。这对促进我国评估行业的健康发展,维护社会主义市场经济秩序,具有十分重要的意义。我国的资产评估是在改革开放中逐步发展起来的。上世纪八十年代,伴随着国有企业改革的深化和国有资产管理体制的创新,资产评估应运而生。近20年来,资产评估对促进国有企业改革、防止国有资产流失、维护国有资产权益,发挥了重要作用。随着我国社会主义市场经济的发展,资产评估发挥着越来越大的作用,它的服务领域已经直接涉…