Optimal combinational quota‐share and excess‐of‐loss reinsurance policies in a dynamic setting

In this paper, we describe a large insurance company's surplus by a Brownian motion with positive drift, which is the approximation of a classical risk process. The problem of minimizing the probability of ruin by controlling the combinational quota‐share and excess‐of‐loss reinsurance strategy is considered. We show that the optimal combinational reinsurance strategy must be the pure excess‐of‐loss reinsurance strategy. Moreover, we give an explicit solution for the optimal reinsurance strategy. Copyright © 2006 John Wiley & Sons, Ltd.     

Minimizing coherent risk measures of shortfall in discrete‐time models with cone constraints

The paper studies the problem of minimizing coherent risk measures of shortfall for general discrete‐time financial models with cone‐constrained trading strategies, as developed by Pham and Touzi. It is shown that the optimal strategy is obtained by super‐hedging a contingent claim, which is represented as a Neyman–Pearson‐type random variable.     

Goal achieving probabilities of cone‐constrained mean‐variance portfolios

In this paper, we establish closed‐form formulas for key probabilistic properties of the cone‐constrained optimal mean‐variance strategy, in a continuous market model driven by a multidimensional Brownian motion and deterministic coefficients. In particular, we compute the probability to obtain to a point, during the investment horizon, where the accumulated wealth is large enough to be fully reinvested in the money market, and safely grow there to meet the investor's financial goal at terminal time. We conclude that the result of Li and Zhou [Ann. Appl. Prob., v.16, pp.1751–1763, (2006)] in the unconstrained case carries over when conic constraints are present: the former probability is lower bounded by 80% no matter the market coefficients, trading constraints, and investment goal. We also compute the expected terminal wealth given that the investor's goal is underachieved, for both the mean‐variance strategy and the aforementioned hybrid strategy where transfer to the money market occurs if it allows to safely achieve the goal. The former probabilities and expectations are also provided in the case where all risky assets held are liquidated if financial distress is encountered. These results provide investors with novel practical tools to support portfolio decision‐making and analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Mean–variance asset–liability management: Cointegrated assets and insurance liability

The cointegration of major financial markets around the globe is well evidenced with strong empirical support. This paper considers the continuous-time mean–variance (MV) asset–liability management (ALM) problem for an insurer investing in an incomplete financial market with cointegrated assets. The number of trading assets is allowed to be less than the number of Brownian motions spanning the market. The insurer also faces the risk of paying uncertain insurance claims during the investment period. We assume that the cointegration market follows the diffusion limit of the error-correction model for cointegrated time series. Using the Markowitz (1952) MV portfolio criterion, we consider the insurer’s problem of minimizing variance in the terminal wealth, given an expected terminal wealth subject to interim random liability payments following a compound Poisson process. We generalize the technique developed by Lim (2005) to tackle this problem. The particular structure of cointegration enables us to solve the ALM problem completely in the sense that the solutions of the continuous-time portfolio policy and efficient frontier are obtained as explicit and closed-form formulas.     

Mean‐variance hedging with basis risk

Basis risk arises in a number of financial and insurance risk management problems when the hedging assets do not perfectly match the underlying asset in a hedging program. Notable examples in insurance include the hedging for longevity risks, weather index–based insurance products, variable annuities, etc. In the presence of basis risk, a perfect hedging is impossible, and in this paper, we adopt a mean‐variance criterion to strike a balance between the expected hedging error and its variability. Under a time‐dependent diffusion model setup, explicit optimal solutions are derived for the hedging target being either a European option or a forward contract. The solutions are obtained by a delicate application of the linear quadratic control theory, the method of backward stochastic differential equation, and Malliavin calculus. A numerical example is presented to illustrate our theoretical results and their interesting implications.     

离散时间单位连结人寿保险合同的局部风险最小对冲策略

单位连结人寿保险合同是保险利益依赖于某特定股票的价格的保险合同。当保险公司发行这样的保险合同后，保险公司将面临金融和被保险人死亡率两类风险。因此这样的保险合同相当对不完全金融市场上的或有索取权，不能利用自我融资交易策略复制出。本提出利用不完全市场的局部风险最小对冲方法对冲保险的风险，我们在离散时间的框架下给出了局部风险最小对冲策略。     

Modeling stock index returns by means of partial least‐squares methods: An out‐of‐sample analysis for three stock markets

We analyze the underlying economic forces of the stock markets in Germany, the U.K. and the U.S. Identifying a number of variables evincing return predictability, we follow a partial least‐squares (PLS) approach to combine these observables into a few latent factors. Conditional on European markets, our findings indicate (i) superior prediction performance of PLS‐based schemes in comparison with both, a random walk and a first‐order autoregressive benchmark model, (ii) consistent profitable trading on the German and British market, (iii) profitable linear forecast combinations, (iv) the U.S. stock market is diagnosed as informationally efficient. Copyright © 2010 John Wiley & Sons, Ltd.     

THE INSURANCE VALUE OF BIODIVERSITY IN THE PROVISION OF ECOSYSTEM SERVICES

ABSTRACT. Biodiversity provides insurance against the uncertain provision of ecosystem services which are being used by risk‐averse economic agents. I present a conceptual ecological‐economic model that combines (i) current results from ecology about the relationships between biodiversity, ecosystem functioning, and the provision of ecosystem services with (ii) economic methods to study decision‐making under uncertainty. In this framework I (1) determine the insurance value of biodiversity, (2) study the optimal allocation of funds in the trade‐off between investing into biodiversity protection and the purchase of financial insurance, and (3) analyze the effect of different institutional regimes in the market for financial insurance on biodiversity protection. I conclude that biodiversity acts as a form of natural insurance for risk‐averse ecosystem managers against the over‐ or under‐provision with ecosystem services. Therefore, biodiversity has an insurance value, which is a value component in addition to the usual value arguments, such as direct or indirect use or non‐use values. In this respect, biodiversity and financial insurance are substitutes. Hence, the availability, and exact institutional design, of financial insurance influence the level of biodiversity protection.     

Knowledge‐based scenario tree generation methods and application in multiperiod portfolio selection problem

A scenario tree is an efficient way to represent a stochastic data process in decision problems under uncertainty. This paper addresses how to efficiently generate appropriate scenario trees. A knowledge‐based scenario tree generation method is proposed; the new method is further improved by accounting for subjective judgements or expectations about the random future. Compared with existing approaches, complicated mathematical models and time‐consuming estimation, simulation and optimization problem solution are avoided in our knowledge‐based algorithms, and large‐scale scenario trees can be quickly generated. To show the advantages of the new algorithms, a multiperiod portfolio selection problem is considered, and a dynamic risk measure is adopted to control the intermediate risk, which is superior to the single‐period risk measure used in the existing literature. A series of numerical experiments are carried out by using real trading data from the Shanghai stock market. The results show that the scenarios generated by our algorithms can properly represent the underlying distribution; our algorithms have high performance, say, a scenario tree with up to 10,000 scenarios can be generated in less than a half minute. The applications in the multiperiod portfolio management problem demonstrate that our scenario tree generation methods are stable, and the optimal trading strategies obtained with the generated scenario tree are reasonable, efficient and robust. Copyright © 2013 John Wiley & Sons, Ltd.     

Explicit portfolio for unit-linked life insurance contracts with surrender option

Introducing a surrender option in unit-linked life insurance contracts leads to a dependence between the surrender time and the financial market. [J. Barbarin, Risk minimizing strategies for life insurance contracts with surrender option, Tech. rep., University of Louvain-La-Neuve, 2007] used a lot of concepts from credit risk to describe the surrender time in order to hedge such types of contracts. The basic assumption made by Barbarin is that the surrender time is not a stopping time with respect to the financial market.The goal of this article is to make the hedging strategies more explicit by introducing concrete processes for the risky asset and by restricting the hazard process to an absolutely continuous process.First, we assume that the risky asset follows a geometric Brownian motion. This extends the theory of [T. Møller, Risk-minimizing hedging strategies for insurance payment processes, Finance and Stochastics 5 (2001) 419–446], in that the random times of payment are not independent of the financial market. Second, the risky asset follows a Lévy process.For both cases, we assume the payment process contains a continuous payment stream until surrender or maturity and a payment at surrender or at maturity, whichever comes first.     

权益连结生存人寿保险合同的局部风险最小对冲策略

权益连结生存人寿保险合同是保险金依赖于某类特定股票的价格的保险合同 .本文主要利用Schweizer[3]引入的不完全市场的局部风险最小理论确定单位关联人寿保险合同的局部风险最小对冲策略 .     

Stochastic optimization for the ruin probability

The Cramér‐Lundberg insurance model is studied where the risk process can be controlled by reinsurance and by investment in a financial market. The performance criterion is the ruin probability. The problem can be imbedded in the framework of discrete‐time stochastic dynamic programming. Basic tools are the Howard improvement and the verification theorem. Explicit conditions are obtained for the optimality of employing no reinsurance and of not investing in the market.     

Risk‐minimizing hedging strategies with restricted information and cost

With the assumption that information cost is characterized by a Poisson process, this paper presents risk‐minimizing problems under jump‐diffusion models. First, the explicit optimal strategy under complete information is given using Itô formula. Second, the optimal strategy problem under restricted information is solved by projection. Copyright © 2009 John Wiley & Sons, Ltd.     

Chances and limitations of a short‐term overreaction effect – stochastic considerations and empirical results

As a specific case of the overreaction phenomenon in financial markets we observe reversals of index and future prices in periods following a suggested “qualified movement” of prices. Such a situation is indicated on the one hand by a monotone growth or decline of closing prices during three trading days. On the other hand, there are formulated stochastic conditions expressing a sufficiently improbable market situation, which is frequently compensated by a significant short‐term price reversal. Reversal measures are discussed and a case study completes the paper.     

Temporal aggregation of Markov‐switching financial return models

In this paper we investigate the effects of temporal aggregation of a class of Markov‐switching models known as Markov‐switching normal (MSN) models. The growing popularity of the MSN processes in modelling financial returns can be attributed to their inherited flexibility characteristics, allowing for heteroscedasticity, asymmetry and excess kurtosis. The distributions of the process described by the basic MSN model and the model of the corresponding temporal aggregate data are derived. They belong to a general class of mixture normal distributions. The limiting behaviour of the aggregated MSN model, as the order of aggregation tends to infinity, is studied. We provide explicit formulae for the volatility, autocovariance, skewness and kurtosis of the aggregated processes. An application of measuring solvency risk with MSN models for horizons larger than 1 year and up to 10 years from the baseline U.S. S&P 500 stock market total return time series spanning about 50 years is given. Copyright © 2008 John Wiley & Sons, Ltd.     

An optimal investment strategy for a stream of liabilities generated by a step process in a financial market driven by a Lévy process

In this paper we investigate an asset-liability management problem for a stream of liabilities written on liquid traded assets and non-traded sources of risk. We assume that the financial market consists of a risk-free asset and a risky asset which follows a geometric Lévy process. The non-tradeable factor (insurance risk or default risk) is driven by a step process with a stochastic intensity. Our framework allows us to consider financial risk, systematic and unsystematic insurance loss risk (including longevity risk), together with possible dependencies between them. An optimal investment strategy is derived by solving a quadratic optimization problem with a terminal objective and a running cost penalizing deviations of the insurer’s wealth from a specified profit-solvency target. Techniques of backward stochastic differential equations and the weak property of predictable representation are applied to obtain the optimal asset allocation.     

On the Modeling of CO2 EUA and CER Prices of EU‐ETS for the 2008–2012 Period

Increased consumption of fossil fuels in industrial production has led to a significant elevation in the emission of greenhouse gases and to global warming. The most effective international action against global warming is the Kyoto Protocol, which aims to reduce carbon emissions to desired levels in a certain time span. Carbon trading is one of the mechanisms used to achieve the desired reductions. One of the most important implications of carbon trading for industrial systems is the risk of uncertainty about the prices of carbon allowance permits traded in the carbon markets. In this paper, we consider stochastic and time series modeling of carbon market prices and provide estimates of the model parameters involved, based on the European Union emissions trading scheme carbon allowances data obtained for 2008–2012 period. In particular, we consider fractional Brownian motion and autoregressive moving average–generalized autoregressive conditional heteroskedastic modeling of the European Union emissions trading scheme data and provide comparisons with benchmark models. Our analysis reveals evidence for structural changes in the underlying models in the span of the years 2008–2012. Data‐driven methods for identifying possible change‐points in the underlying models are employed, and a detailed analysis is provided. Our analysis indicated change‐points in the European Union Allowance (EUA) prices in the first half of 2009 and in the second half of 2011, whereas in the Certified Emissions Reduction (CER) prices three change‐points have appeared, in the first half of 2009, the middle of 2011, and in the second half of 2012. These change‐points seem to parallel the global economic indicators as well. Copyright © 2016 John Wiley & Sons, Ltd.     

Shooting at the poachers while the rhinos drown: Managing short‐ and long‐term threats to endangered wildlife in conservation reserves

This paper addresses management challenges associated with conserving endangered wildlife facing multiple threats from illegal poaching, habitat encroachment, and climate and land‐use change‐induced flooding. While poaching and encroachment challenges in conservation parks are of immediate nature, climate‐related risks exist in the long term. The park manager faces a utility function that includes as its arguments local community’s incomes, benefits to the larger society from preserving threatened species and the financial costs of monitoring and land‐use change efforts. Using the case of single‐horned rhinos in the Kaziranga National Park, India, an optimal mix of monitoring and land‐use changes is designed in presence of tradeoffs between short‐ and long‐term management efforts. As monitoring only addresses immediate challenges associated with poaching and encroachment, long‐term climatic risks remain ignored. Land‐use management offers risk‐protection as well as risk‐insurance benefits with respect to climate change‐induced flooding of the park. Recommendations for Resource Managers

• It is important to incorporate both short‐ and long‐term risks posed to endangered wildlife while investing in conservation efforts. There may exist a tradeoff between mitigating short‐ and long‐run risks due to financial and physical resource constraints. However, ignoring long‐term risks to wildlife habitats can jeopardize past conservation efforts.
• Land‐use management, both within and outside of conservation reserves, enhances resilience to climatic shocks through reducing flooding risks and must be an essential part of wildlife conservation efforts.
• Conservation efforts ignoring local community welfare considerations can become suboptimal as they lead to reduced cooperation and potential conflicts. When wildlife conservation efforts account for local community welfare implications, optimal management plans could result in lower species abundance in the short term. However, increasing the park size through additional land enrollment can mitigate some of this tradeoff.

     

Application of the phase‐type mortality law to life contingencies and risk management

The class of phase‐type distributions has recently gained much popularity in insurance applications due to its mathematical tractability and denseness in the class of distributions defined on positive real line. In this paper, we show how to use the phase‐type mortality law as an efficient risk management tool for various life insurance applications. In particular, pure premiums, benefit reserves, and risk‐loaded premiums using CTE for standard life insurance products are shown to be available in analytic forms, leading to efficient computation and straightforward implementation. A way to explicitly determine provisions for adverse deviation for interest rate and mortality is also proposed. Furthermore, we show how the interest rate risk embedded in life insurance portfolios can be analyzed via interest rate sensitivity index and diversification index which are constructed based on the decomposition of portfolio variance. We also consider the applicability of phase‐type mortality law under a few non‐flat term structures of interest rate. Lastly, we explore how other properties of phase‐type distributions may be applied to joint‐life products as well as subgroup risk ordering and pricing within a given pool of insureds. Copyright © 2017 John Wiley & Sons, Ltd.     

Asymptotic finite‐time ruin probabilities for a class of path‐dependent heavy‐tailed claim amounts using Poisson spacings

In the compound Poisson risk model, several strong hypotheses may be found too restrictive to describe accurately the evolution of the reserves of an insurance company. This is especially true for a company that faces natural disaster risks like earthquake or flooding. For such risks, claim amounts are often inter‐dependent and they may also depend on the history of the natural phenomenon. The present paper is concerned with a situation of this kind, where each claim amount depends on the previous claim inter‐arrival time, or on past claim inter‐arrival times in a more complex way. Our main purpose is to evaluate, for large initial reserves, the asymptotic finite‐time ruin probabilities of the company when the claim sizes have a heavy‐tailed distribution. The approach is based more particularly on the analysis of spacings in a conditioned Poisson process. Copyright © 2010 John Wiley & Sons, Ltd.