Study On Technological Innovation Investment Decisions: Options Game Approach

As far as firms are concerned, the velocity and intensity of technological innovations have become the two key elements to measure firms'achievements, competitive power and the potential for development. Also, technological innovations have brought firms lots of overwhelming investment opportunities. However, these investment opportunities are accompanied with the uncertainty of technologies themselves, the contradictions of the displacement between the new technology and the old one and competition of the homogeneous technologies in the market. Besides, firms who have implemented technological innovations are often not single, so fierce competition exists among them. Thus, a firm must adopt flexible management strategies to invest and produce according to market conditions, rival's actions and technological development states, etc.. Options game approach deeply applying mathematical tools, such as stochastic analysis, optimal stopping times, martingale, stochastic differential equations, stochastic optimal control, game theory, etc., overcomes the drawbacks of traditional methods, combines corporate finance, management science and investment decisions and has formed a set of new strategic investment management methods of firms'technological innovation investment decisions and has more and more applications in both theoretic and realistic aspects of corporate decision-making analysis. This thesis applies options game approach to study several problems related to firms'technological innovation investment. Chapter 1 first introduces some main contents and research methods of firms'technological innovation investment, then outlines and analyzes current research situations on the application of options game approach to study firms'technological innovation investment. From chapter 2 on, research contents are as follows: 1. Study of basic theories on two kinds of probability formulas. Chapter 2 studies two kinds of probability formulas which are often used in finance science, especially in financial investment science. It enriches their theoretic bases, improves their proof methods and extends some results of them. The following study will reflect their applications of some theoretic results in Chapter 2. The benchmark formula of the first kind of probability formulas is formula (2-15). Firstly, drifted Brownian motion is considered, where it combines the reflection principal of Brownian motion with Girsanov's theorem of measure-changing, uses joint density atom to derive marginal density atom, then gets marginal density function and obtains formula (2-15) and some useful corollaries. Here the approach using joint density atom to derive marginal density atom to derive marginal density is easier to apply, for it can avoid tedious derivations and calculations related to marginal density function. Secondly, it extends formula (2-15) to the circumstance of geometric Brownian motion by means of It?'s lemma. The benchmark formula of the second kind of probability formulas is formula (2-39). Firstly, it defines several events and sets by the definition of stopping times, then proves a preliminary lemma and derives formula (2-39) by means of the reflection principle and preliminary lemma and extends formula (2-39) to the circumstance of drifted Brownian motion. Secondly, it extends formula (2-39) to the circumstance of geometric Brownian motion by means of It?'s lemma. 2. Applied study on two kinds of probability formulas. Basing on some relevant literature, Chapter 3 gives applied frameworks in financial investment science of two kinds of probability formulas studied in Chapter 2. The first kind are mainly used in the investment models containing investment options, and here a common framework of a problem of leader-follower investment times'interval is formulated, which will be applied in the following study. As to the comprehensive applications of the two kinds, Chapter 3 bases on existing models to outline two frameworks: a probability problem of investment goals'attainment and a problem of a kind of pricing exotic options. 3. Study of basic models on symmetrical duopoly under uncertainty. Chapter 4 studies Huisman & Kort model which has important historical positions and extensive applications, where it follows the original framework of Huisman & Kort model, but calculates and introduces the value function and investment threshold of monopoly firm and improves the proof method of all kinds of investment thresholds'comparison. Finally, it discusses emphatically mixed-strategies equilibrium's applications and collusion equilibriums without a binding contract and points out that collusion investment is not a equilibrium in Smets/ Dixit &Pindyck model, while it is a perfect Nash equilibrium which is destroyed if the first-mover advantage is sufficiently large and reasonable simulations based on some parameters can explain this. 4. Developing study of basic models by introducing operating costs and exogenous technological innovations. Chapter 5 considers a dynamic duopoly model in which two firms compete in the adoption of current technology with a further new technology anticipated. Here it is assumed that operating costs are not zero which has more explanatory power of the real world. Its aim is to find the impact of the velocity of technological innovations or substitutions and the introduction of operating costs on firms'investment strategies. Three kinds of equilibriums may occur in the adoption of the current technology, which mainly depends on the level of operating costs and the first-mover advantage. It draws an idea in technological innovation science that the faster technological substitutions or innovations encourage the leader to invest earlier while induces the follower to invest later. Furthermore, a new result is obtained: like the investment costs, with the increase of the operating costs, the follower tends to invest later while the leader tends to invest earlier, and the investment thresholds are more sensitive to the change of the operating costs than that of the investment costs. Using mixedstrategies analysis, competitive investment strategies with sequential exercise and simultaneous exercise are derived. 5. Considering firstly operating cost asymmetry and technological innovation time factor comprehensively and deeply analyzing asymmetric duopoly under uncertainty. Chapter 6 applies options game approach to study firms'technological innovation investment decisions with asymmetric operating cost under imperfect competition, discusses emphatically the impact of firms'operating cost asymmetry and required time to implement technological innovations successfully on technological innovation investment, obtains leader and follower's value functions and corresponding investment thresholds and derives the preemptive, sequential and simultaneous investment equilibrium. It firstly applies options game approach to analyze comprehensively firms'operating cost asymmetry and required time to implement technological innovations successfully, which indicates that operating cost asymmetry and required time to implement technological innovations successfully are the main reasons that affect the three kinds of equilibriums above. Besides, the first-mover advantage may affect them under some conditions. The impact of operating cost asymmetry and required time to implement technological innovations successfully on the average time interval of the firms'investment is analyzed under preemptive and sequential investment equilibrium,and the main results are as follows: under preemptive equilibrium, when the first-mover advantage is sufficiently large, the change of the average time interval of the firms'investment is opposite to the change of operating cost asymmetry, while the relation between average time interval of the firms'investment and required time to implement technological innovations successfully is characterized by ambiguity; under sequential equilibrium, the impact of the change of operating cost asymmetry and required time to implement technological innovations successfully on the change of the average time interval of the firms'investment displays in two opposite directions. 6. Interface with other directions and discussion about the impact of firms'technological innovation investment decisions on macroeconomic growth and fluctuations. Chapter 7 develops a model of growth and fluctuations that are both driven by the -from time to time-arrival of new technologies. Its aim is to study the relation between technological innovation investment and economic growth as well as fluctuations, to analyze the main factors that may affect firms'technological innovation investment decisions and the impact of the uncertainty on economic growth and fluctuations. No matter how the new technology arrives in the home country, through innovational activities or by way of imitation, the intermediate firms decide when or whether to adopt (or implement) these technologies. To adopt a new technology requires an irreversible investment, depending on the size of barriers to technology adoption, and yields a higher average growth rate of productivity for some period time. Due to the assumed uncertainty in the evolution of the productivity and the irreversible nature of theinvestment, there exists an option value of waiting for better but never complete information. This translates into a critical level of the productivity parameter, such that waiting is optimal if the actual productivity lies between that level, and investing takes place as soon as the productivity parameter reaches that level. It firstly studies firms'heterogeneity, firms'technological investment decisions, economic growth and fluctuations in a same framework, which shows that if firms are homogeneous, then technological innovations stimulate the average economic growth rate to increase a higher level; on the contrary, if firms are heterogeneous, then the increase of technological innovations on the average economic growth rate is more gradual and slower. Furthermore, the impact of the uncertainty of current technology and new technology on the technological innovation investment and the average economic growth displays different ways: the change of the uncertainty of new technology is the same as that of the investment threshold of technological innovation and different from that of the average economic growth, while the relation between the change of the uncertainty of current technology and the change of the two above is characterized by ambiguity.