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 Chinese citizens, proposing that personal risk management in China follows a typical "three generations integrated" model. In this context, it distinguishes the personal risk management concepts and characteristics of different groups, discussing the resulting life insurance consumption patterns and their future trends. By further examining the personal risk situations and consequences of Chinese citizens, it reveals some concerning issues in the characteristics of personal risk management models. Based on this foundation, it employs quantitative methods to study the innovation and optimization design of life insurance products for the characteristics of personal risk management models in China. It points out that life insurance products are essentially the result of individuals comparing and weighing multiple 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 finds that the life insurance products demanded by the public constitute a typical complex adaptive system, and thus constructs a genetic algorithm model to quantify the process of life insurance product innovation and optimization design. On this basis, it explores the dynamic life insurance pricing problem with stochastic investment return decision objectives. For this purpose, it briefly introduces the necessary foundational theories. As a prerequisite for constructing life insurance pricing theory, it focuses on introducing backward stochastic differential equations and their comparison theorems. Then, from several aspects, it studies the no-arbitrage life insurance pricing model with stochastic investment return decision objectives. 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 themselves but also its hedging and no-arbitrage approaches are suitable for other fund investments—as long as the expected return objectives 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, purchasing insurance can be seen as hedging against the premiums paid. The insurer, on the other hand, must invest the premiums collected to achieve expected investment returns. On one hand, it must determine the amount of premiums collected, and on the other hand, it must 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 concept of "hedging." However, according to traditional life insurance pricing methods, pricing and investment are separate, with hedging considerations at most being taken into account during the investment process. This not only seems rigid but also has strong limitations. In light of this, this book specifically studies the no-arbitrage life insurance pricing method. The pricing philosophy of this method has 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 manifested 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, which are achieved through investment. If all premiums are invested in risky assets, although the expected return can be calculated using the historical return rate, this calculated expected return includes risk factors and cannot be guaranteed. However, if a portion of the same premiums is allocated to risky investments while another portion is invested in risk-free assets to offset the risk, then through reasonable design, under the condition of dynamically satisfying the value equation of life insurance pricing, a given expected payout amount can be guaranteed. 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 situation of the investment market, and the pricing process has strong operability.
(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 refer to the financial market situation when considering the minimum return on their investment in insurance, but they do not truly care about the insurer's actual investment situation or various costs and 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 and still receive some protection against personal risks. Of course, the acceptable cost is a slightly lower return on investment. For the insurer to better understand this purpose quantitatively, as a basis for evaluating whether the insurer's pricing is feasible, it is important to simulate the policyholder's situation. The goal is to make life insurance pricing relatively fair, make the policies more acceptable to policyholders, and increase the success rate of insurance products. Since the insurer's decision-making objectives must include both the expected payout target for the insured and the company's profit target, and the amount available for investment is only the net premium after deducting various costs, the insurer's decision-making process—i.e., how much premium to charge and how to invest—needs to be addressed. The research here considers both the supply and demand sides within the same investment system, adhering to the principle of individual fairness, and conducts no-arbitrage life insurance pricing from the perspectives of both sides.
(3) Targeted No-Arbitrage Life Insurance Pricing Method in Practice In view of the widespread application of asset allocation pricing methods in practice and their shortcomings in reflecting investment, this section improves the asset allocation pricing method on the basis of the aforementioned no-arbitrage life insurance pricing method, obtaining a dynamic asset allocation pricing method. It not only inherits the excellent performance of the asset allocation pricing method but also achieves the goal of making the premium and its structure reflect dynamic investment conditions. All the pricing methods mentioned above provide corresponding examples, simulation analysis, and discussions to demonstrate the interaction between the insurance market and the financial market during the pricing process.