Dynamic Game Theoretic Models in Marketing and Finance
This dissertation deals with Differential Games (DG) and its application in general Market and Financial Market. It has three parts. Chapters 1-3 deal with optimal competition strategies for
general product. I break up the normal product life cycle into three sub-stage life cycles, set up non-cooperative DG model for each sub-stage life cycle, derive optimality conditions for it,
which in general is a set of Boundary Value Problems(BVPs) or Differential-Algebraic Equations(DAE), and design algorithms to solve it. One of the algorithms is based on full discretization, and is first-order convergent, the other algorithm is based on Shooting method and Random Perturbation technique, and belongs to quasi-Newton method. From the numerical results, I contrast the difference between open-loop and closed-loop controls. In Chapters 4-5, I set up Leader-Follower DG and cooperative DG for marketing competition. The motivation for these two special kinds of games comes from practical considerations. In Chapter 4, I use Calculus
of Variation to derive a system of optimality conditions for Leader-Follower DG, and design an algorithm to solve it. The algorithm is random, and second order convergent. In Chapter 5, I set up cooperative DG model, and adopt Evolutionary Algorithm(EA) to solve the model. From the numerical results, I compare the above three kinds of DG, and draw practical guidelines. Chapter 6-7 deal with Stochastic Differential
Games(SDG). In chapter 6, I set up SDG model for general market competition, and derive a set of optimality conditions using Dynamic Programming(DP). The set of optimality condition consists of
Stochastic Partial Differential Equations(SPDE). Then, I design algorithm to solve the SPDE. In chapter 7, I extend SDE to financial marketing.
I regard the pricing process as SDE between option seller and buyer, then I set up SDE model for option pricing. Finally, I derive optimality conditions for the pricing model.
Advisor:Negash Medhin; Zhilin Li; Tao Pang; Ivan T. Kandilov
School:North Carolina State University
School Location:USA - North Carolina
Source Type:Master's Thesis
Date of Publication:07/15/2008