Equilibrium mean–variance reinsurance and investment strategies for a general insurance company under smooth ambiguity

This work investigates the equilibrium investment and reinsurance strategies for a general insurance company under smooth ambiguity. The general insurance company holds shares of an insurance company and a reinsurance company. The claims of the insurer follow a compound Poisson process. The insurer can divide part of the insurance risk to the reinsurer. Besides, the insurer and reinsurer both participate in the financial market and invest in cash and stock. However, the general insurance company is ambiguous about the insurance and financial risks and is an ambiguity-averse manager (AAM). The uncertainties over the insurance and financial risks are described by second-order distributions. The AAM aims to maximize the average performance of the weighted sum surplus process of the insurer and reinsurer under the mean–variance criterion and smooth ambiguity. We present the extended Hamilton–Jacobi–Bellman (HJB) system for the optimization problem combining the mean–variance criterion and smooth ambiguity. In the case that the second-order distributions are Gaussian, we obtain the closed-forms of the equilibrium reinsurance and investment strategies. At the end of this work, sensitivity analyses are presented to show the economic behaviors of the AAM.     

Optimal investment and reinsurance policies for an insurer with ambiguity aversion

In this paper, we study the optimal investment and reinsurance problem for an insurer based on the variance premium principle, in which three cases are considered. First, we assume that the financial market does not exist. The insurer only holds an insurance business, and the optimal reinsurance problem is studied. Subsequently, we assume that there exists a financial market with an accurately modeled risky asset. The optimal investment and reinsurance problem is investigated under these conditions. Finally, we consider the general case in which the insurer is concerned about the model ambiguity of both the insurance market and the financial market. In all three cases, the value function is set to maximize the expected utility of terminal wealth. By employing the dynamic programming principle, we derive the Hamilton–Jacobi–Bellman (HJB) equations, which are satisfied by the value functions and obtain closed-form solutions for optimal reinsurance and investment policies and the value functions in all three cases. Most interestingly, we elucidate how investment improves the insurer’s utility and find that the existence of ambiguity can significantly affect the optimal policies and value functions. We also compare the ambiguities in the two markets and find that ambiguity in the insurance market has much more significant impact on the value function than the ambiguity in the financial market. It implies that it is more valuable for insurer to precisely evaluate the insurance risk. We also provide some numerical examples and economic explanations to illustrate our results.     

Optimal time-consistent reinsurance and investment strategies for a jump–diffusion financial market without cash

This paper considers an optimal reinsurance and investment strategies for an insurer under mean–variance criterion within a game theoretic framework. Specially, it is assumed that the surplus process is governed by a Cramér–Lundberg model, and apart from purchasing reinsurance, the insurer is allowed to invest in a financial market with multiple assets that all can be risky, whose price processes are modeled by the jump–diffusion process. Due to the market without cash, the method of separating the variables is not viable any more. We turn to an alternative approach to solve the extended Hamilton–Jacobi–Bellman equation, and closed-form expressions of the optimal strategies and value function are not only derived but also proved to be uniqueness. Moreover, some special cases of our model are provided and several numerical analyses for our results are presented as well. Under this criterion, different from existing literature, we find that (i) the value function is not linear but quadratic with respect to the current wealth; (ii) the optimal reinsurance and investment strategies depend on the wealth process; (iii) the parameters of risky assets(insurance market) have impacts on the optimal reinsurance(investment) policy; (iv) the safety loading of the insurer affects the optimal strategies.     

Time-consistent investment and reinsurance strategies for insurers under multi-period mean-variance formulation with generalized correlated returns

The existing literature on investment and reinsurance is limited to the study of continuous-time problems, while discrete-time problems are always ignored by researchers. In this study, we first discuss a multi-period investment and reinsurance optimization problem under the classical mean-variance framework. When the asset returns with a serially correlated structure, the time-consistent investment and reinsurance strategies are acquired via backward induction. In addition, we propose an alternative time-consistent mean-variance optimization model that contrasts with the classical mean-variance model, and the corresponding optimal strategy and value function are also derived. We find that the investment and reinsurance strategies are both independent of the current wealth for the above two optimization problems, which coincides with the conclusion presented in the continuous-time problems. Most importantly, the above investment strategies with serially correlated structures are both conditional mean-based strategies, rather than unconditional ones. Finally, we compare the investment and reinsurance strategies suggested above based on the simulation approach, to shed light on which investment-reinsurance strategies are more suitable for insurers.     

Ambiguity on the insurer’s side: The demand for insurance

Empirical evidence suggests that ambiguity is prevalent in insurance pricing and underwriting, and that often insurers tend to exhibit more ambiguity than the insured individuals (e.g., Hogarth and Kunreuther, 1989). Motivated by these findings, we consider a problem of demand for insurance indemnity schedules, where the insurer has ambiguous beliefs about the realizations of the insurable loss, whereas the insured is an expected-utility maximizer. We show that if the ambiguous beliefs of the insurer satisfy a property of compatibility with the non-ambiguous beliefs of the insured, then optimal indemnity schedules exist and are monotonic. By virtue of monotonicity, no ex-post moral hazard issues arise at our solutions (e.g., Huberman et al., 1983). In addition, in the case where the insurer is either ambiguity-seeking or ambiguity-averse, we show that the problem of determining the optimal indemnity schedule reduces to that of solving an auxiliary problem that is simpler than the original one in that it does not involve ambiguity. Finally, under additional assumptions, we give an explicit characterization of the optimal indemnity schedule for the insured, and we show how our results naturally extend the classical result of Arrow (1971) on the optimality of the deductible indemnity schedule.     

国外财务再保险会计对我国的启示

财务再保险作为一种非传统的风险转移方式,常被保险公司作为优化会计报表财务安排或金融工具。目前我国缺乏关于财务再保险的企业会计准则,会给一些滥用财务再保险的保险公司以可趁之机。因此,必须对我国财务再保险会计处理进行研究。本文在介绍国外财务再保险会计确认和会计处理的基础上,结合我国具体情况,对规范我国财务再保险的会计处理提出了政策建议。     

The restricted convex risk measures in actuarial solvency

In this article, we propose a class of convex risk measures defined on appropriate wedges of a space of financial positions which denote the cumulative surplus variables created by undertaking risks by either an insurance or a reinsurance company. The form of the wedge which is the domain of such a risk measure expresses the form of the company, and it is a subspace in the case of reinsurance companies and a cone in the case of the insurance companies. The value of such a risk measure on an insurance position denotes the capital that the corresponding company has to receive or to keep in advance so that it will not be exposed to risk due to this position. We prove some dual representation and continuity results being similar to the unrestricted case. Finally, we contribute to a decision theory related to the choice of a numeraire asset when the space in which the positions lie in is reflexive.     

Mean-variance portfolio selection of cointegrated assets

This paper considers the continuous-time mean-variance portfolio selection problem in a financial market in which asset prices are cointegrated. The asset price dynamics are then postulated as the diffusion limit of the corresponding discrete-time error-correction model of cointegrated time series. The problem is completely solved in the sense that solutions of the continuous-time portfolio policy and the efficient frontier are obtained as explicit and closed-form formulas. The analytical results are applied to pairs trading using cointegration techniques. Numerical examples show that identifying a cointegrated pair with a high mean-reversion rate can generate significant statistical arbitrage profits once the current state of the economy sufficiently departs from the long-term equilibrium. We propose an index to simultaneously measure the departure level of a cointegrated pair from equilibrium and the mean-reversion speed based on the mean-variance paradigm. An empirical example is given to illustrate the use of the theory in practice.     

具有奖励机制与再保险安排的最优保险合约设计

在保险合约中引入奖励机制可以使投保人动态参与到保险合约中,赋予了投保人在面对索赔事件时是否执行索赔的可选择权,改变了传统保险合约中投保人执行索赔的单一权利,但却增加了保险人潜在的流动性风险。保险合约中再保险的安排则可以对冲由于奖励机制产生的潜在流动性风险,进一步分散保险人的风险,有助于保险人稳健经营。基于此,通过建立具有红利奖励机制与再保险安排的最优保险合约设计模型,最终求解得到最优保险合约是具有最优免赔额形式的保险合约。利用算例研究方法进行建模,研究结果显示,最优保险合约中的最优免赔额与奖励机制中的红利奖励之间具有正向关系,保费、自留额与最优免赔额之间则存在着显著的负向关系。     

Contingent factors of the coinsurance function of internal capital markets: Evidence from the US nonlife insurance industry

By analyzing intragroup reinsurance activities in the US nonlife insurance sector from 1999 to 2016, we provide evidence that the coinsurance function of internal capital markets is contingent on internal capital providers’ financial resources and the relative sizes of capital receivers within the group. We demonstrate that insurance groups commonly use intragroup reinsurance (a substitute for capital) to support insurers that sustain underwriting losses. Larger insurers are more likely to obtain internal reinsurance if their affiliated insurers hold more financial resources. Our findings show that the financial capabilities of group members providing support affect the feasibility of the coinsurance function through the activities of internal capital markets. Group members with greater influence are more likely to benefit from the coinsurance function.     

金融行业间的资产风险外溢影响

银行业、保险业和证券业因投资业务而构建起联系，并基于金融资产价格而具有了传染渠道。随着投资活动愈发频繁，金融行业中各行业内部的资产风险可能外溢至其他行业。本文首先从理论上分析金融行业资产风险通过投资资产外溢的过程，通过搭建资产抛售模型模拟资产风险的传染机制，从机构层面和行业层面分析资产风险的生成与传递。其次，基于金融机构实际数据的模拟分析结果显示，四大国有商业银行和中国平安具有外溢风险的能力，首先影响银行和保险公司，随后再扩散到整个金融行业，而证券业则相对较为独立。银行业的外溢影响最大，其次是保险业和证券业。但事实上很难发生足以对外部造成显著影响的损失事件。资产、投资比例、杠杆和监管要求水平在资产风险外溢的过程中具有一定的影响。     

Cross-hedging minimum return guarantees: Basis and liquidity risks

We reveal pitfalls in the hedging of insurance contracts with a minimum return guarantee on the underlying investment, e.g. an external mutual fund. We analyze basis risk entailed by hedging the guarantee with a dynamic portfolio of proxy assets for the funds. We also take account of liquidity risk which arises since the insurer may need to advance funds for performing the hedge. Based on a least-squares Monte Carlo simulation, we study the economic implications of basis and liquidity risks. We demonstrate that both risks may be surprisingly high and show how the design of the contract and the hedging strategy may help to alleviate them.     

Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk

According to the classic no arbitrage theory of asset pricing, in a frictionless market a No Free Lunch dynamic price process associated with any essentially bounded asset is a martingale under an equivalent probability measure. However, real financial markets are not frictionless. We introduce an axiomatic approach of Time Consistent Pricing Procedure (TCPP), in a model free setting, to assign to every financial position a dynamic ask (resp. bid) price process. Taking into account both transaction costs and liquidity risk this leads to the convexity (resp. concavity) of the ask (resp. bid) price. We prove that the No Free Lunch condition for a TCPP is equivalent to the existence of an equivalent probability measure R that transforms a process between the bid price process and the ask price process of every financial instrument into a martingale. Furthermore we prove that the ask (resp. bid) price process associated with every financial instrument is then a R super-martingale (resp. R sub-martingale) which has a càdlàg version.     

Catering to investors through capital expenditures: Testing assets substitution problem around financing

We test the catering theory, which describes how investor preferences might influence individual firms' investment financing decisions. To the best of our knowledge, our study may well be the first that directly connects catering with asset substitution to contrast the magnitude of catering by bondholders and shareholders. And indeed, it is interesting to find that although catering behavior is found to exist among both corporate bond and seasoned equity offering (SEO) managers, the coexistence of both appears to offset the abnormal investment phenomena of either underinvestment or overinvestment. The study results further reveal that firms engage in overinvestment when catering to conversion holders of existing convertible bonds. Taken together, we find that support for the asset substitution and abnormal investment argument is strong from a stockholder–bondholder conflict.     

Optimal rebalance rules for the constant proportion portfolio insurance strategy – Evidence from China

The constant proportion portfolio insurance (CPPI) strategy is one of the most popular asset allocation strategies employed by guaranteed-return financial products investors. Rebalance disciplines play an important role in determining the CPPI performance in practice. This paper examines whether the selection of rebalance rules affects CPPI strategy performance in the context of Chinese equity markets and, if so, in what pattern, and whether an optimal parameter of rebalance exists. We find that, (1) the three alternative rebalance disciplines – time discipline, market move discipline and lag discipline – are indifferent in affecting the performance of CPPI strategy; (2) in terms of optimal parameters of each rebalance rule, the optimal rebalancing period for the time discipline is 3 trading days, the optimal trading threshold of the market move discipline 4%, and the optimal lag factor of the lag discipline 6%. These optimal parameters are not influenced by the length of investment.     

寿险公司盈余管理研究——基于业务特性驱动视角

寿险公司业务经营具有跨期均衡性、资金融通性、偿付能力充足性三大特性。受业务特性驱动,寿险公司盈余管理策略具有独特性,这些策略主要包括再保险交易、保险准备金提取、金融资产分类和计量。合理适度的盈余管理有利于维护寿险公司和保险市场的稳定发展。     

Are generalized call-spreads efficient?

In order to explain coexistence of a deductible for low values of the loss and an upper limit for high values of the loss in insurance contracts, we consider the exchange of risk between two rank dependent expected utility maximizers. It is shown that if the insurer (insured) takes more into account the lowest outcomes – hence maximal losses – than the insured (insurer), then the optimal contract has an upper limit (includes a deductible for high values of the loss). If furthermore, the insured (insurer) neglects the highest outcomes while the insurer (insured) does not, the optimal contract includes a deductible (full insurance) for low values of the loss.     

Market selection of constant proportions investment strategies in continuous time

This paper studies the wealth dynamics of investors holding self-financing portfolios in a continuous-time model of a financial market. Asset prices are endogenously determined by market clearing. We derive results on the asymptotic dynamics of the wealth distribution and asset prices for constant proportions investment strategies. This study is the first step towards a theory of continuous-time asset pricing that combines concepts from mathematical finance and economics by drawing on evolutionary ideas.     

Behavior patterns of investment strategies under Roy’s safety-first principle

The safety-first principle is a natural motivational factor in decision making, and is closely related to certain popular heuristics such as satisficing. We provide a systematic analysis of optimal portfolio choice under Roy’s safety-first principle by examining and comparing the behavior patterns of three popular investment strategies: the optimal constant-rebalanced portfolio, dynamic-rebalanced portfolio and buy-and-hold strategies. Our results indicate the importance of a match between the investment strategy, the investment goal, and the investment horizon. We also develop a geometric approach to investigate the relationships among the safety-first, expected utility, and mean-variance models and offer an explanation for the long-standing debate concerning different patterns of time-diversification effects.