تخصیص دارایی مطلوب برای یک مجموعه کلی از سیاست های بیمه عمر

Asset liability matching remains an important topic in life insurance research. The objective of this paper is to find an optimal asset allocation for a general portfolio of life insurance policies. Using a multi-asset model to investigate the optimal asset allocation of life insurance reserves, this study obtains formulae for the first two moments of the accumulated asset value. These formulae enable the analysis of portfolio problems and a first approximation of optimal investment strategies. This research provides a new perspective for solving both single-period and multiperiod asset allocation problems in application to life insurance policies. The authors obtain an efficient frontier in the case of single-period method; for the multiperiod method, the optimal asset allocation strategies can differ considerably for different portfolio structures.

This article attempts to investigate optimal asset allocations in a stochastic investment environment for a general portfolio of life insurance policies. Asset liability matching remains an important issue for long-term liabilities, such as insurance policies or pension funds. Most insurance companies’ assets consist of policyholders’ premiums, such that each policy represents a specific liability for the insuring firm. Thus, maximizing investment returns may not be the primary goal of insurance companies, which may instead be more concerned with managing policyholders’ premiums, such that returns adequately meet future benefits or guarantee profits to policyholders. Besides, insurance policies offered by insurers also vary in duration, so it is not realistic to discuss only the case of asset liability management for a single policy. Therefore, we consider asset liability management in a more general case in which random policy durations exist in a product’s profile. In this paper, we investigate the asset allocation issue on life insurance reserves. Previous research focuses on studying the distribution of reserves, from one policy (e.g. Panjer and Bellhouse, 1980, Bellhouse and Panjer, 1981 and Dhaene, 1989) to portfolios (e.g. Waters, 1978, Parker, 1994a, Parker, 1994b and Marceau and Gaillardetz, 1999). They examine the distribution of life insurance reserves in a specific interest rate model, for example, AR(1) model or ARCH(1) model. We introduce a multi-asset model and consider the asset allocation problem of life insurance companies. For the asset allocation issue, widespread investigations consider the investment strategy for a single-period approach (e.g. Hurlimann, 2002, Sharpe and Tint, 1990, Sherris, 1992, Sherris, 2006, Wilkie, 1985, Wise, 1984a, Wise, 1984b, Wise, 1987a and Wise, 1987b), whereas multiperiod asset allocations in discrete time rarely have been explored. Extensive research into the optimal multiperiod investment strategy concentrates mostly on continuous time models with dynamic controls (e.g. Chiu and Li, 2006 and Emms and Haberman, 2007) or uses the martingale method (e.g. Wang et al., 2007). With these approaches, the optimal strategy takes the new information generated by filtration, but to solve the closed form solution in discrete time, they often suffer from mathematical complexity and intractability. Another approach is to get the numerical solution by stochastic programming (see Dempster, 1980 and Carino et al., 1994). It overcomes the disadvantage of finding theoretical solution. The model can be constructed easily and realistically. However, it faces other problems. Stochastic programming constructs the possible asset return scenario by trees. A good description about the market depends on the number of nodes at each decision point. On the other hand, the time cost has an exponential growth as does the number of nodes. Thus, for the purpose of finding the solution in a tolerable time, the node number is often insufficient to describe the real market. Consequently, it is inevitable for the existence of large approximation error. Thus, to examine the appropriate investment strategy in discrete time, we must trade off between the convenience of the method and the accuracy of the solution. Specifically, we examine two kinds of rebalancing methodologies: constant rebalancing and variable rebalancing. At the beginning of every year, the portfolio mix gets realigned according to one of these two methods. Constant rebalancing means that the portfolio mix should realign to a constant proportion of assets, or the single-period method. Variable rebalancing implies that the portfolio mix realigns with a different proportion of assets each time, or the multiperiod method. A continuing business line contains some mature polices and some new policies every year, so the single-period method is more suitable than a multiperiod method, because of the ongoing new policies. If the number of mature polices is close to the number of new policies, the structure of the policy portfolio remains similar between two neighboring decision dates. Therefore, it would be reasonable to adopt a constant rebalance strategy and retain the same weight of assets in a stable proportion every year. If the number of mature polices differs from the number of new policies, the durations of the policy portfolios should differ every year. Therefore, the proportion of constant rebalance requires recalculation, according to the updated durations of policy portfolios every year. Occasionally, a business line ceases to exist, so no new policies occur in the future. In this case, variable rebalancing with a multiperiod method is suitable for matching the rest of the periods of the liabilities. Because insurance policies typically involve a long duration of more than five years, choosing the optimal investment strategies is crucial to ensure that insurance companies can maximize their profits while reducing their insolvency risk. We propose an optimization approach for analyzing the optimal portfolio problem for both single-period and multiperiod asset allocations. In turn, we propose an optimization approach to generate the optimal investment strategy of an asset liability management model for long-term endowment policies. The proposed discrete time investment model includes both static, single-period and multiperiod optimal investment strategies for a time-dependent asset return process. We derive the formulae for the first and second moments of the accumulated asset value of the insurer based on a multi-asset return model. With these formulae, we can analyze the portfolio problems for both single-period and multiperiod methods. For the single-period method, we depict an efficient frontier under a constant rebalance strategy, which can be determined from arbitrary policy portfolios. In the case of the multiperiod method, we obtain a first approximation of the optimal asset allocation, as applied to a ceased life insurance product line. The numerical results show that the proportion of cash should increase when we compare a portfolio with uniform years before maturity with a portfolio comprised of new policies. In Section 2, we formulate the explicit form of the first two moments of accumulated asset value, followed by the mean-variance analysis and an investigation of the optimal asset allocation strategy for various policy portfolios in Section 3. We then examine the parameter sensitivities and discuss the large sample problem in Section 4. Finally, we give the conclusion in Section 5.

As Campbell and Viceira (2002) indicate, there are several important developments in the long-term portfolio choice area recently. These include computing power and numerical method, discovery of new closed form solution and access from approximate analytical solutions. In our study, we approximate the actual portfolio return by Log-normal random variable, which makes the moments tractable. We derive the formulae for the moments of the accumulated asset value of the insurer, and then get the numerical results by numerical method. Hence, we find the optimal asset allocation by numerical method, but also exploit the advantage from the approximate analytical method. This paper successfully derives the formulae of the first and second moments of accumulated asset value based on a multi-asset return model. With these formulae, we can analyze portfolio problems and obtain optimal investment strategies. Therefore, this research provides a new perspective on solving both single-period and multiperiod asset allocation problems, as applied to life insurance policies. We investigate the optimal asset allocation with both the constant and variable rebalancing methods. For constant rebalancing, we find an efficient frontier in the mean–standard deviation plot that occurs with arbitrary policy portfolios. The insurance company should hold more cash to reduce its illiquidity risk for portfolios in which policies will mature at earlier dates. In the case of variable rebalancing, we find that the optimal asset allocation strategy can differ considerably, given different portfolio structures. Thus, it is important for an insurance company to find a suitable investment strategy for different policy portfolios. In the present model, we calculate the liability reserve exogenously for simplicity. In practice, the reserve should be valued on the market basis according to the requirement of various countries. In addition, nowadays the life insurance authorities in various countries require that a certain amount of money needs to be set aside as capital at the end of each year. These two issues are important and unavoidable in practice. It is somewhat difficult to take these two issues into account and we ignore these two issues in this paper. However, in practice if the market information can be acquired, the insurance company is able to value the liabilities on the market basis. It can obtain the reserve from the market information and then find the optimal asset allocation strategy by applying the method proposed in this paper. Moreover, an insurer can estimate the distribution of the accumulated asset value through simulation and so can know the probability of failing the authority’s requirement. By adjusting the value of the parameter kk (risk-tolerant parameter) in the objective function, one can find a conservative investment strategy that achieves an authority’s requirement.