Analysis Of Decision Making Under Risk

Risk is the core concept of finance theory, any branch of which can be ascribed to the problem of risk management and pricing. Dealing with risk is the most important things in the business for any kinds of institution in financial sector, bank, insurances or securities company are the same in this sense. Even in our daily life, we would always make decisions under risk. So, analysis of decision making under risk is of interest both theoretically and practically. However, do we really comprehensive risk? How much we know about our risk attitudes?The paradigm of modern economics is expressing and solving economic issues using mathematics. Then, we must have a utility function as the starting point. Most of advanced models in finance theory are based on the work of von Neumann and Morgenstern, known as Expected Utility function. Under EU, risk aversion is equivalent to the concavity of value function, and individuals can only have one kind of the three risk attitudes——risk aversion, risk pursuing or risk neutral. But, we often observe multiple risk attitudes in a single one in reality. There can be other elements affecting risk attitudes which are omitted in EU. Actually, behavioral economists have already reached accordance opinions about this problem. Among which the best know work must be Kahneman and Tversky (1979) and Tversky and Kahneman (1991), and my work just base on theirs.In Chapter1, I declare the frequently used notations and concepts, make clear about my contributions and the threads of writing.In Chapter2, we will review the related literatures both home and oversees. Domestic literatures mainly focused on the empirical researches in the view of PT. Rarely seen theoretical researches about the foundation theory in the field of decision making under risk. Internationally, topic about decision making under risk are hot issues. There are great many related literatures theoretically, empirically and experimentally. I will introduce those theories competing with PT, and theories extending it, empirical and experimental works based on it. In Chapter3, I will introduce EU from my angle, exploring graphics and charts to explain the ideas of theoretical concepts, such as, Independence Axiom, Simplex, Compound Lotteries, Stochastic Dominance, Certainty Equivalence, etc. By doing this, we can grasp the other related theories quickly and smoothly. Most of competing theories tried to modify the Independence Axiom. They regard the failure of Independence Axiom as the reason of some experiment results violating EU. In my theory, I also add some restrictions on Independence Axiom. Simplex is a particular graph depicting indifference curve on Lottery Space. I can show intuitively the difference of two theories via comparing EU’s and GPT’s Simplex. Compound Lotteries is a conception closely pertained to dynamic problems, which I talk about as surveying the convex combination of Lottery Space. The validity of stochastic dominance is discussed under the framework of GPT. EU is the classical theory regarded as a benchmark theory to judge the various competing behavioral theories. Re-examining about EU would do good for further researches.In Chapter4, display the series of experiments in PT to see how Kahneman and Tversky category man’s mental effects under risk. The style of chapter4is totally disparate with that of chapter3. If chapter3is an abstract one, then chapter4must be a concrete one. When we familiar with the whole thesis and re-check the experiment problems, we may feel there are some inappropriateness in the category of mental effects. But I choose to keep the original way of classifying. Because it represents natural course by which we recognize ourselves. I want to emphasize two of several mental effects, reference effects and nonlinear weighting manner. In a word, chapter4deserves a carefully reading for its heuristic experiments.In Chapter5, Cumulative Prospect Theory equip with the property of rank dependent, then it can overcome some flaws haunted with Prospect Theory, making it extend to continuous form, and respect first order stochastic dominance. Rank dependent refers to the weight of some contingent state is not only concerned with its own probabilities, but also probabilities of other states matter. I summarize the process of GPT’s proof, and make a comment. Experiment eliciting individuals’ certainty equivalent to estimate the parametric model is also introduced.In Chapter6, we find the imperfection of the axiomatic foundations of GPT via discussing Sure Thing Principle, Double Matching, Comonotonicity. I maintain the first three axioms in EU, and add other three as the axiomatic foundations of GPT. Employing simple mathematic tools, I derive the function form of GPT. It keeps the descriptive power, meanwhile, obtain more solid backgrounds. And I propose a new form of value function, talk over its intuition as follow. In end, we show how to solve Allais paradox and Ellsberg paradox from the way of GPT.In Chapter7, we aim to compare GPT’s value function and CPT’s value function. I deem the financial status is a crucial factor affecting man’s risk attitudes. CPT does not include this crucial factor, while GPT do it. So, we conduct similar experiments with GPT’s, collect one more variable, wealth data. In fact, we use the students’one term consumption as the instrument variable of their wealth status. Fortunately, the results favor our anticipation. In addition, we test several corollaries in GPT, and probe the demographic characteristic concerning to risk attitudes using this dataset.In Chapter8, empirical test of arbitrage pricing is arranged as the complementary of previous researches. The work of theory and experiments need to presume we know about the information of contingent outcomes and corresponding probabilities. In real markets, the information does not state out. We test whether arbitrage is an useful guideline for us to extrapolate the movements of asset price. Specifically, I take advantage of the routine halt in our stock market to eliminate endogeneity, and get positive outcome.In Chapter9, as a conclusion of the thesis, I make clear the three most prominent factors affecting risk attitudes, loss aversion, nonlinear and rank dependent weighting function, curvature of value function. In the last place, I talk about the links of GPT with several classical theories.