On The Pricing Theory Of The Risk Assets Based On The Principle Of Essential Arbitrage Is Not Allowed

Most results of the traditional finance theory were based on the principle of no arbitrage opportunity exists. By studying the simplest risk asset FC (flip a coin): you pay one dollar to obtain the right of flipping a coin, if the face appears, you get 3 dollars returned; if the tail appears, you get nothing and lose the dollar you paid. We found that if the coin is fair, you will be able to start from a very small capital, say ?> 0, by means of legal trading, to obtain a very large profit, say A/ < , with a probability very close to 1, say 1 - a. \Ve will call this situation an opportunity of essential arbitrage. We feel that it is unreasonable to consider such a financial market \&perfect. So in this dissertation, we introduce the principle of essential arbitrage is not allowed to replace the traditional principle of no arbitrage opportunity exists as a standard for the financial market being perfect. Obviously, arbitrage is stronger than essential arbitrage; so essential arbitrage is not allowed is stronger than no arbitrage. What is the key difference? Under some very general conditions, we prove that due to the principle of essential arbitrage is not allowed, any risk asset has uniquely a reasonable price, and the probability' distribution of the return about a risk asset must be a risk neutral probability distribution. As we know, the principle of no arbitrage opportunity exists is unable to ensure that any risk asset has uniquely a reasonable price, the simplest risk asset FC mentioned above, for example, may have any price in (0, 3) without violating this principal (of course, in the same financial market, a risk asset can not have two difference prices). Due to the un-uniqueness of the price about the basic risk asset, the pricing of its derivative assets is not based on the real probability distribution of the (random) return of the basic risk asset, but based on the so-called risk-neutral probability which depends on the price of the basic risk asset. Clearly the probability law of the return for a derivative asset (associated with the basic risk asset) depends only on the real probabilityindistribution of the (random) return of the basic risk asset (this is surely unique), nothing related to the Artificial risk-neutral probability. Don't you think this is un-consistent? As a result, people may take different attitudes toward the risks, even the same person may take different attitudes toward different risks (from different risk assets), and the traditional theory has been established mainly for the risk aversion people, i.e., the rational investors are all risk aversion, while the risk favor people are speculators. Based on the principle of essential arbitrage is not allowed, the correct attitude toward risks is just to ignore, either aversion or favor will create chance of essential arbitrage for others.The whole dissertation has been divided into four chapters. Chapter 1 discusses the simplest financial market consist of only one basic risk asset FC and one risk-free asset NFC, the later just means keeping your money in your pocket without any really trading. But we will see, with only these two basic assets, the market contains fruitful derivative assets. Chapter 2 discusses the simple financial market consist of only one basic risk simple asset (as a random variable, its return is simple, i.e., takes only finitely many different values) and one risk-free asset. Chapter 3 discusses the general financial market consist of only one basic risk asset and one risk-free asset. The first 3 chapters discuss the two basic assets financial market (one risk asset, and one risk-free asset). While the last chapter, chapter 4: other topics, includes: the investment wheel, the multi-period risk asset, multi-period risk estate with decision making, and binary lattice stock option.