Life Insurance Product Optimization Theory - Models and Methods

Author: Shi Yufeng
Publisher:
Publish Date: 2006-06-01
Features: This book explores the characteristics of personal risk management models for the Chinese public, proposing that personal risk management for the Chinese public is a typical "three-generations-integrated" model. In this sense, it distinguishes the personal risk management concepts and characteristics of different groups, discusses the life insurance consumption situations and trends resulting from these differences, and further examines the personal risk management model to reveal some concerning issues. Based on this, it employs quantitative methods to study the innovation and optimization design of life insurance products for the personal risk management model of the Chinese public. It points out that the essence of life insurance products is the result of people's decisions to compare and weigh various factors that can form a policy based on their life philosophies and practical conditions. To make insurance resources fully utilized, it emphasizes that product innovation should be separated from the product pricing process to allow for theoretical research. From a scientific perspective, it is found that the life insurance products demanded by the public constitute a typical complex adaptive system. Therefore, a genetic algorithm model is constructed to quantify the process of life insurance product innovation and optimization design. On this basis, it explores the dynamic life insurance pricing problem with a stochastic investment return decision goal. For this, it briefly introduces the necessary theoretical foundations. As a prerequisite for constructing the life insurance pricing theory, it focuses on introducing backward stochastic differential equations and their comparison theorems. Then, it studies the no-arbitrage life insurance pricing model with a stochastic investment return decision goal from several aspects. As the core content, the study of the no-arbitrage life insurance pricing model is the most important part of this book. Considering that not all risky investments can necessarily take the form of options (in fact, most do not, especially in underdeveloped investment markets like China), the "hedging" concept and "no-arbitrage" approach of option pricing theory cannot be directly applied to the pricing of non-option-form risky assets, including life insurance pricing. Therefore, the targeted research conducted in this section is not only important for life insurance pricing methods but also its hedging and no-arbitrage approaches are suitable for other fund investments—as long as the expected return goals are appropriately limited, various investment portfolio forms can be tested to select investment products that meet the investment requirements. Thus, this no-arbitrage pricing method has certain general significance. Below, a brief introduction to this section is provided.
(1) Basic Research on No-Arbitrage Life Insurance Pricing Method From the policyholder's perspective, the act of purchasing insurance can be seen as hedging against the premiums paid. The insurer, on the other hand, must invest the premiums collected to achieve the expected investment returns. To do so, it must determine the amount of premiums collected and decide the structure of the premiums, i.e., the proportion of premiums allocated to risky investments. Given the solvency requirements of life insurance, the insurer's decision-making process must also reflect the "hedging" concept to ensure future payouts. However, according to traditional life insurance pricing methods, pricing and investment are separate, with hedging only considered during the investment process at best. This approach is not only rigid but also highly limited. Given this reality, this book specifically studies the no-arbitrage life insurance pricing method. The pricing philosophy of this method shares similarities with option pricing theory from the perspectives of "hedging" and "no-arbitrage," and the conclusions drawn are comparable to the Black-Scholes formula①, but it is not a simple application of the Black-Scholes formula. This method is specifically implemented as follows: the insurer pays the policyholder an expected payout amount at a future time. The expected payout amount can be considered as the premiums collected at the present time, invested and grown. If all premiums are invested in risky assets, although the expected return can be calculated using the historical return rate, this return includes risk factors and cannot be guaranteed. However, if a portion of the premiums is allocated to risky investments while another portion is invested in risk-free assets to offset the risk, through reasonable design, it is possible to dynamically satisfy the value equation of life insurance pricing while ensuring a given expected payout amount. By establishing a dynamic pricing model, this no-arbitrage life insurance pricing process can be implemented through hedging. Clearly, the price thus determined directly adapts to the conditions of the investment market, and the pricing process has strong operational feasibility.
(2) No-Arbitrage Life Insurance Pricing Method Based on Individual Fairness Principle Life insurance pricing should adhere to the principle of individual fairness. Simply using market equilibrium price theory for pricing is not objective. Policyholders will consider a general minimum return on their investment in insurance based on market conditions, without truly caring about the insurer's actual investment situation, various expenses, or profits. Their purpose of purchasing insurance is somewhat similar to investing in a fund, but they hope to bear less investment risk than a fund while also receiving some protection against personal risks. Of course, the acceptable trade-off is a slightly lower return on investment. The insurer would ideally gain a quantitative understanding of this purpose to assess the feasibility of their pricing. It is true that this quantification process is not actually performed by the policyholder but is rather a simulation by the insurer of the policyholder's situation, with the goal of making life insurance pricing more fair, making policies more acceptable to policyholders, and increasing the success rate of insurance products. Since the insurer's decision-making objectives must include both the expected payout goals for the insured and the company's profit goals, and the amount available for investment is only the net premium after deducting various expenses, the insurer must decide how to set premiums and invest, which is the problem to be addressed. This research places both the supply and demand sides within the same investment system and considers them together, adhering to the principle of individual fairness and using the hedging concept to conduct no-arbitrage life insurance pricing from both sides of the supply and demand.
(3) Targeted No-Arbitrage Life Insurance Pricing Method in Practice Given the widespread application of asset share pricing methods in practice and their shortcomings in reflecting investment conditions, this section improves the asset share pricing method on the basis of the aforementioned no-arbitrage life insurance pricing method to obtain the dynamic asset share pricing method. It not only inherits the excellent performance of the asset share pricing method but also achieves the goal of making premiums and their structures reflect dynamic investment conditions. All of the pricing methods mentioned above provide corresponding examples, simulations, and discussions to demonstrate the interaction between the insurance market and the financial market during the pricing process. By further exploring the personal risk situations and consequences of the Chinese public, this book reveals some concerning issues in the characteristics of the personal risk management model.