Option Game Analysis Of Insurance

Combining the respective theoretical advantages of both option pricing theory and game theory, option game approach focuses on analyzing the dynamic multi-person decision making problems in continuous time and under uncertainty. In essence, this approach uses the option pricing technique to determine the value of players' payoffs related to contingent claims, and to solve the dynamic game in the sequence of players' moves. Option game approach replaces the maximization of expected utility encountered in classic game theory models with the maximization of the value of an option, which gives the arbitrage-free value of the payoffs to the player and can therefore be considered as a proxy for expected utility. Over the expected-utility approach, the option-pricing approach has the advantage that it automatically takes the time value of money and the price of risk into account. This approach is very useful in the analysis in that complex decision problems under uncertainty can be solved by applying classical optimization procedures (minimization and maximization) to the value of the option. The analysis then often boils down to finding a first-order condition for a maximum or minimum.At the moment, in financial decision literature virtually no attempt has been made to integrate game theory aspects, i.e. strategic financial decision of the agents, into the continuous time framework. In this doctoral dissertation, the author attempts to apply the option game analysis framework to the study of insurance issue, this is mostly because insurance products and many insurance decision making problems are characteristic of "contingent claims" more or less. Insurance market, just like its financial counterpart, is full of risk and uncertainty, which provides the opportunity of application of option game theory based on framework of continuous-time finance to insurance field. Using such method, this dissertation focuses on the analyses of property-liability insurance pricing, insurance company's capital structure, as well as pricing of life insurance contracts embedded implicit option elements. Including seven chapters, this dissertation's structure is as follows:Chapter 1 introduces the backgrounds and meaning of the study, and comprehensively summarizes domestic and international literature in relation totheory of option game and application of option pricing in insurance. The last part of this chapter introduces main contents and innovation of this thesis.Chapter 2 provides some basic theory necessary for understanding the option game and insurance theory. Section 1 introduces research contents and development tendency of insurance theory and insurance economics, and Section 2 option theory and its pricing methods. Section 3 reviews basic theory of dynamic game, including basic elements of a game., conception of equilibrium and the way to solve a game.Chapter 3 develops a framework of option game analysis of insurance. In section 1 option game analysis method in continuous time is introduced, and then the general framework of option game theory and its application procedure. Section 2 presents option pricing models in insurance. First, the author introduces a basic option pricing model based on single period and single line of business in property-liability insurance and its extension, i.e. option pricing model of multi-line business. Next, the problem of allocation of equity capital and claims of insurer and the insured on insurance company also are discussed. Finally, fair valuation model of life insurance contract embedded implicit option element is introduced. Section 3 summarizes some notable issues of application of option game in insurance.Chapter 4 applies option game method to property-liability insurance, mainly focusing on fair valuation of excess-of-loss reinsurance and deductible insurance. Section 4.1 exams the difference between finance pricing and actuarial pricing, as well as their relations, and then indicates the essence of financial pricing of insurance. Section 4.2, firstly, proposes some criteria of economic valuation models, secondly, it gives a taxonomy of valuation models, and finally argues valuation models needed for insurance liability pricing. In section 4.3, fair valuation of deductible insurance is discussed. The author develops a basic model and makes an extension which studies changes of the insured's strategy and equilibrium insurance price in the presence of "bonus-malus system". The last section analyzes the option-like feature of excess-of-loss reinsurance, and gives an arbitrage-free value and optimal retention of excess-of-loss reinsurance policy.Chapter 5 studies the optimal capital structure and bankruptcy decision of insurance company. Section 1 simply analyzes the interest claims of insurance agents on insurance company, where equity value of shareholder can be viewed as a call option and the insured's claims, i.e. the fair value of insurance, a put option. Section 5.2 introduces insurance guaranty funds system and its implication to insurancesolvency regulation. Under insurance guaranty funds system with risk-based premium, Section 5.3 prices value of equity and insurance guarantee, and thus of social welfare, using option pricing technique, respectively, and then in dynamic game theory framework analyzes insurance guarantor's liquidation strategy and insurer's financing and investment strategies. In this model, bankruptcy decision is endogenous. In the following section 5.4, a more general case is analyzed, which incorporates the following assumptions: insurance guaranty funds system based on "flat-rate" premium prevailing in insurance practice, limited company life, bankruptcy decision made by owner, the presence of tax, and so on. Under such assumptions, the values of claims of owner, insurer and the insured can be calculated with option pricing technique, thus the optimal bankruptcy decision, incentive feature of the owner, the optimal insurance liability issuance amount and optimal insurance guarantee premium rate can be derived. The last section summarize this chapter.Turning to another insurance field, life insurance, chapter 6 develops a option game model dealing with fair valuation of equity-linked life insurance policies (ELLIPs). Section 6.1 creates a basic model using risk-neutral option pricing technique for fair valuation of ELLIPs which embeds interest guarantee and free surrender, where the optimal surrender strategy of the insured comes down to finding a optimal stop-timing. In this section some new developments in American option pricing theory are used to derive the "quasi" closed form solution to value of basic contract. In the following, numerical simulation and comparative static analysis are made, thus indicating the property of surrender option. The next section 6.2 emphasizes another approach, i.e. partial differential equation approach, to solve the optimal surrender boundary of the insured. In this model mortality benefit is introduced, which reflects the actuarial element. First of all, the surrender boundary, when contract is close to maturity, is calculated approximately, and then other surrender boundaries at the point of time elsewhere are derived by numerical analysis. Given the time interval small enough, a continuous surrender boundary can be depicted. The last part is a summary of chapter 6.Chapter 7 summarizes the whole thesis, and points out its defects and future improvements.