Contingent claim pricing using probability distortion operators: methods from insurance risk pricing and their relationship to financial theory

This paper considers the pricing of contingent claims using an approach developed and used in insurance pricing. The approach is of interest and significance because of the increased integration of insurance and financial markets and also because insurance-related risks are trading in financial markets as a result of securitization and new contracts on futures exchanges. This approach uses probability distortion functions as the dual of the utility functions used in financial theory. The pricing formula is the same as the Black-Scholes formula for contingent claims when the underlying asset price is log-normal. The paper compares the probability distortion function approach with that based on financial theory. The theory underlying the approaches is set out and limitations on the use of the insurance-based approach are illustrated. The probability distortion approach is extended to the pricing of contingent claims for more general assumptions than those used for Black-Scholes option pricing.     

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.     

Risk analysis with categorical explanatory variables

To better forecast the Value-at-Risk of the aggregate insurance losses, Heras et al. (2018) propose a two-step inference of using logistic regression and quantile regression without providing detailed model assumptions, deriving the related asymptotic properties, and quantifying the inference uncertainty. This paper argues that the application of quantile regression at the second step is not necessary when explanatory variables are categorical. After describing the explicit model assumptions, we propose another two-step inference of using logistic regression and the sample quantile. Also, we provide an efficient empirical likelihood method to quantify the uncertainty. A simulation study confirms the good finite sample performance of the proposed method.     

Tweedie’s Compound Poisson Model With Grouped Elastic Net

Tweedie’s compound Poisson model is a popular method to model data with probability mass at zero and nonnegative, highly right-skewed distribution. Motivated by wide applications of the Tweedie model in various fields such as actuarial science, we investigate the grouped elastic net method for the Tweedie model in the context of the generalized linear model. To efficiently compute the estimation coefficients, we devise a two-layer algorithm that embeds the blockwise majorization descent method into an iteratively reweighted least square strategy. Integrated with the strong rule, the proposed algorithm is implemented in an easy-to-use R package HDtweedie, and is shown to compute the whole solution path very efficiently. Simulations are conducted to study the variable selection and model fitting performance of various lasso methods for the Tweedie model. The modeling applications in risk segmentation of insurance business are illustrated by analysis of an auto insurance claim dataset. Supplementary materials for this article are available online.     

On pricing and reserving with-profits life insurance contracts

As a first approximation, asset and liability management issues faced by life insurance companies originate from the sale of with-profits contracts. These contracts are bond-type products with several rate guarantees and other interestsensitive embedded options. Benefits paid out to policyholders mostly depend on the investment performance of a given asset portfolio in which premiums are invested. Thus, guarantees and options granted to policyholders may become effective when the investment performance of the asset portfolio is poor. Issuing a with-profits contract is therefore not equivalent to issuing plain-vanilla debt. The purpose of this paper is to value with-profits liabilities in a consistent option-pricing framework and to develop efficient asset or liability strategies to manage profitability and variability of shareholder value.     

On the refracted–reflected spectrally negative Lévy processes

We study a combination of the refracted and reflected Lévy processes. Given a spectrally negative Lévy process and two boundaries, it is reflected at the lower boundary while, whenever it is above the upper boundary, a linear drift at a constant rate is subtracted from the increments of the process. Using the scale functions, we compute the resolvent measure, the Laplace transform of the occupation times as well as other fluctuation identities that will be useful in applied probability including insurance, queues, and inventory management.     

基于动态财务分析的地质灾害保险定价

将经济学中的动态财务分析(DFA)模型应用于地质灾害保险定价中,对离散的灾害事件、经济损失等进行建模分析,计算出纯保费.实证分析以湖南省邵阳市为例,结果表明该模型实用性强、操作简单,计算出来的保费率具有一定的参考价值.     

Poisson Approximation of Impulsive Recurrent Process with Semi-Markov Switching

In this article, the weak convergence of impulsive recurrent process with semi-Markov switching in the scheme of Poisson approximation is proved. Singular perturbation problem for the compensating operator of the extended Markov renewal process is used to prove the relative compactness.     

Finite time ruin probabilities for tempered stable insurance risk processes

We study the probability of ruin before time t$t$ for the family of tempered stable Lévy insurance risk processes, which includes the spectrally positive inverse Gaussian processes. Numerical approximations of the ruin time distribution are derived via the Laplace transform of the asymptotic ruin time distribution, for which we have an explicit expression. These are benchmarked against simulations based on importance sampling using stable processes. Theoretical consequences of the asymptotic formulae indicate that some care is needed in the choice of parameters to avoid exponential growth (in time) of the ruin probabilities in these models. This, in particular, applies to the inverse Gaussian process when the safety loading is less than one.     

保险动态惩罚机制对网约车平台监督作用的演化博弈研究

采用演化博弈方法,研究保险公司与网约车平台之间的博弈演化过程,分析了在保险公司监督下,网约车平台策略选择的影响因素,并比较了静态惩罚机制和动态惩罚机制下网约车平台与保险公司博弈的均衡策略。研究发现,保险公司的惩罚性保费可以促使网约车平台的策略选择发生改变。在静态惩罚机制下,网约车平台和保险公司的策略选择呈周期波动模式,不能收敛;在动态惩罚机制下,网约车平台和保险公司的博弈呈现螺旋收敛的演化轨迹,且收敛的均衡点不随策略选择的初始概率不同而改变。研究结论明确了保险在网约车行业管理中的社会监督职能,并为保险公司保费的制定提供理论参考。