平衡损失下约束线性回归模型中回归系数的可容许估计

本文在平衡损失函数下得到等式约束模型中回归系数在齐次(非齐次)估计类中存在可容许估计的充要条件,给出带有不完全椭球约束模型中回归系数的线性估计在一切估计类中为可容许估计的充要条件.     

连续区间策略下二人零和对策问题研究

考虑连续区间策略下的二人零和对策问题,研究其均衡策略的存在性。首先分析了完全信息下的二人零和对策问题,证明了该问题均衡策略的存在性并给出求解方法。然后进一步研究了收益函数不确定的不完全信息二人零和对策问题,在各局中人都认为对方是风险厌恶型的假设下,分析该类对策纯策略均衡的存在性,并通过研究纯策略均衡存在的充要条件给出判断并寻找纯策略均衡解的方法。最后给出一个数值算例,验证本文所提出方法的可行性。     

不完全信息动态二维价格博弈模型及其分析

单位生产成本为不完全信息条件下,本文首先讨论了两个企业关于具有一定替代性的两种产品价格的动态二维博弈模型,并求得其精练Bayes均衡.然后分析了当两种产品不存在替代关系时,企业对这两种产品价格进行动态博弈的精练Bayes均衡相当于对这两种产品单独进行博弈的精练Bayes均衡的简单组合.     

保险与再保险及市场对冲稳健均衡策略

假设保险公司的资本盈余过程服从复合Poisson风险跳过程,保险公司通过向再保险公司购买比例再保险来分散保险风险,保险公司和再保险公司均基于方差原则收取保险费率.两个公司都可以投资于金融市场,其中风险资产的价格过程服从几何布朗运动.假设保险公司和再保险公司都是模糊厌恶的且具有指数效用函数,基于保险公司与再保险公司加权终期财富效用最大化目标,利用动态规划原理,得到了两公司的稳健均衡比例再保险和投资组合策略的解析表达式.分析了均衡条件下的风险投资,再保险价格与保险公司自保险比例受不同参变量影响的变化特征.     

基于套期保值的双寡头零售商供应链均衡策略分析

考虑一个供应商和两个零售商构成的供应链,零售商在面对市场需求风险时决策是否采用套期保值来规避风险.文章分别分析了Cournot和Bertrand两种博弈情景.研究表明:两种博弈存在相同的纳什均衡,两个零售商都会采取套期保值策略.在Cournot博弈下,零售商通过套期保值能够为供应商带来更多的利润;而在Bertrand博弈下,零售商选择套期保值却会降低供应商的利润.相比Cournot博弈,供应商在Bertrand博弈下获利更高.     

免赔额保险公平定价的期权博弈分析

传统保险定价实质上是供给方定价,忽视了保险契约是保险人和投保人双方互动决策的结果.另一方面,保单具有或有权益的性质,这使得近年来金融定价方法得以引入到保险定价中,以反映风险和回报之间的长期均衡关系.借助期权博弈框架引入博弈论和期权定价理论,分析了免赔额保险的公平定价问题,给出了基本模型和扩展模型两种情形下博弈均衡结果,即保单的无套利价值,并发现在扩展模型情形下,投保人的最优投保策略和均衡保险合同均发生变化.     

不完全信息下两个内部交易者的交易行为分析

当市场上存在两个拥有不完全信息的内部交易者时,研究了其对待风险的态度分别为风险喜好、风险中性与风险厌恶情况下模型在混合策略空间中离散时间的均衡解和高频交易下均衡的渐近行为特征,并分析了相关模型的经济金融学意义.     

伪造风险损失欺诈博弈与最优保险合同设计

运用不完全信息动态博弈和机制设计的有关理论，建立了伪造风险损失欺诈博弈模型，研究了伪造风险损失欺诈博弈问题的纳什均衡及其保险双方的最优博弈策略。在此基础上，得出了使保险人的期望利润为零的保险定价公式，讨论了基于保险双方最优博弈策略的最优保险合同形式，证明了基于保险双方最优博弈策略的保险合同是部分保险。     

竞争与合作统一框架下的鲁棒最优再保险策略

在实际中,多个保险人之间经常存在竞争与合作.文章在竞争与合作统一框架下,研究了鲁棒最优再保险策略.每个保险人的盈余过程满足扩散逼近保险模型,n个保险人的索赔之间存在相依关系,每个保险人通过再保险减少索赔风险.文章主要的研究目标是,在最坏市场环境下,寻找最优均衡再保险策略最大化终端财富的均值同时最小化其方差.通过使用随机动态规划和随机控制理论,求得了鲁棒最优均衡再保险策略、最优市场策略和最优值函数的显式解,并从理论上探讨了最优策略的经济意义.最终,通过数值实验分析了竞争、合作、模糊厌恶和风险厌恶对鲁棒最优均衡再保险策略的影响.文章的研究结果可以有效地指导保险人的实践.     

竞争环境下风险规避的航班动态定价

以同一航线上的多个竞争航班为研究对象,在假设各竞争航班之间具有完全信息的基础上,利用马尔可夫决策过程和博弈论,建立了竞争环境下风险规避的航班动态定价的数学模型,证明了均衡价格的存在性。在此基础上,进一步讨论了信息不完全情况下风险规避的竞争航班的动态定价问题。数值实验表明:在竞争环境下,各风险规避航班的均衡价格随自身剩余座位数量和风险规避系数的增加而下降,随其他竞争航班的剩余座位数量和风险规避系数的增加而提高。     

Insurance valuation: A computable multi-period cost-of-capital approach

We present an approach to market-consistent multi-period valuation of insurance liability cash flows based on a two-stage valuation procedure. First, a portfolio of traded financial instrument aimed at replicating the liability cash flow is fixed. Then the residual cash flow is managed by repeated one-period replication using only cash funds. The latter part takes capital requirements and costs into account, as well as limited liability and risk averseness of capital providers. The cost-of-capital margin is the value of the residual cash flow. We set up a general framework for the cost-of-capital margin and relate it to dynamic risk measurement. Moreover, we present explicit formulas and properties of the cost-of-capital margin under further assumptions on the model for the liability cash flow and on the conditional risk measures and utility functions. Finally, we highlight computational aspects of the cost-of-capital margin, and related quantities, in terms of an example from life insurance.     

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??It is assumed that both an insurance company and a reinsurance company adopt the variance premium principle to collect premiums. Specifically, an insurance company is allowed to investment not only in a domestic risk-free asset and a risky asset, but also in a foreign risky asset. Firstly, we use a geometry Brownian motion to model the exchange rate risk, and assume that the insurance company could control the insurance risk by transferring the insurance business into the reinsurance company. Secondly, the stochastic dynamic programming principle is used to study the optimal investment and reinsurance problems in two situations. The first is a diffusion approximation risk model and the second is a classical risk model. The optimal investment and reinsurance strategies are obtained under these two situations. We also show that the exchange rate risk has a great impact on the insurance company's investment strategies, but has no effect on the reinsurance strategies. Finally, a sensitivity analysis of some parameters is provided.     

Optimal Investment-Reinsurance Strategy with Exchange Rate Risk under Variance Premium Principl

It is assumed that both an insurance company and a reinsurance company adopt the variance premium principle to collect premiums. Specifically, an insurance company is allowed to investment not only in a domestic risk-free asset and a risky asset, but also in a foreign risky asset. Firstly, we use a geometry Brownian motion to model the exchange rate risk, and assume that the insurance company could control the insurance risk by transferring the insurance business into the reinsurance company. Secondly, the stochastic dynamic programming principle is used to study the optimal investment and reinsurance problems in two situations. The first is a diffusion approximation risk model and the second is a classical risk model. The optimal investment and reinsurance strategies are obtained under these two situations. We also show that the exchange rate risk has a great impact on the insurance company's investment strategies, but has no effect on the reinsurance strategies. Finally, a sensitivity analysis of some parameters is provided.     

Optimal Cross Hedging of Insurance Derivatives

Abstract

We consider insurance derivatives depending on an external physical risk process, for example, a temperature in a low dimensional climate model. We assume that this process is correlated with a tradable financial asset. We derive optimal strategies for exponential utility from terminal wealth, determine the indifference prices of the derivatives, and interpret them in terms of diversification pressure. Moreover, we check the optimal investment strategies for standard admissibility criteria. Finally, we compare the static risk connected with an insurance derivative to the reduced risk due to a dynamic investment into the correlated asset. We show that dynamic hedging reduces the risk aversion in terms of entropic risk measures by a factor related to the correlation.     

Quantitative modeling of risk management strategies: Stochastic reserving and hedging of variable annuity guaranteed benefits

Variable annuities are enhanced life insurance products that offer policyholders participation in equity investment with minimum return guarantees. There are two well-established risk management strategies in practice for variable annuity guaranteed benefits, namely, (1) stochastic reserving based on risk measures such as value-at-risk (VaR) and conditional-tail-expectation (CTE); (2) dynamic hedging using exchange-traded derivatives. The latter is increasingly more popular than the former, due to a common perception of its low cost. While both have been extensively used in the insurance industry, scarce academic literature has been written on the comparison of the two approaches. This paper presents a quantitative framework in which two risk management strategies are mathematically formulated and where the basis for decision making can be determined analytically. Besides, the paper proposes dynamic hedging of net liabilities as a more effective and cost-saving alternative to the common practice of dynamic hedging of gross liabilities. The finding of this paper does not support the general perception that dynamic hedging is always more affordable than stochastic reserving, although in many cases it is with the CTE risk measure.     

Optimal investment-reinsurance policy for an insurance company with VaR constraint

This paper investigates an investment-reinsurance problem for an insurance company that has a possibility to choose among different business activities, including reinsurance/new business and security investment. Our main objective is to find the optimal policy to minimize its probability of ruin. The main novelty of this paper is the introduction of a dynamic Value-at-Risk (VaR) constraint. This provides a way to control risk and to fulfill the requirement of regulators on market risk. This problem is formulated as an infinite horizontal stochastic control problem with a constrained control space. The dynamic programming technique is applied to derive the Hamilton-Jacobi-Bellman (HJB) equation and the Lagrange multiplier method is used to tackle the dynamic VaR constraint. Closed-form expressions for the minimal ruin probability as well as the optimal investment-reinsurance/new business policy are derived. It turns out that the risk exposure of the insurance company subject to the dynamic VaR constraint is always lower than otherwise. Finally, a numerical example is given to illustrate our results.     

Optimal dynamic asset allocation of pension fund in mortality and salary risks framework

In this paper, we consider the optimal dynamic asset allocation of pension fund with mortality risk and salary risk. The managers of the pension fund try to find the optimal investment policy (optimal asset allocation) to maximize the expected utility of terminal wealth. The market is a combination of financial market and insurance market. The financial market consists of three assets: cashes with stochastic interest rate, stocks and rolling bonds, while the insurance market consists of mortality risk and salary risk. These two non-hedging risks cause incompleteness of the market. By martingale method and dynamic programming principle we first derive the approximate optimal investment policy to overcome the difficulty, then investigate the efficiency of the approximation. Finally, we solve an optimal assets liabilities management(ALM) problem with mortality risk and salary risk under CRRA utility, and reveal the influence of these two risks on the optimal investment policy by numerical illustration.     

A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy

Methodology and Computing in Applied Probability - Risk measures for tail risk have an important application in the dynamic portfolio insurance strategies. We propose a new risk measure called...