Risk-neutral measure

About: Risk-neutral measure is a research topic. Over the lifetime, 990 publications have been published within this topic receiving 25997 citations. The topic is also known as: Risk-neutral probability.

THE DEMAND FOR RISKY ASSETS: Some Extensions

Abstract: Publisher Summary This chapter discusses some extensions on the demand for risky assets. The research on capital asset pricing has until very recently been devoted almost exclusively to the interrelationships of the risk premiums among different risky assets rather than to the determinants of the market price of risk. Such research has also generally relied on theoretical preconceptions to determine the appropriate utility functions of individual investors upon which both the market price of risk and the pricing of individual risky assets depend. The chapter discusses the highlights of the theoretical and empirical analysis and their conclusions. Then, the same analytical framework is used to obtain new results on the effect of inflation on the market price of risk. It turns out that by using nominal values for returns, the market price of risk under inflation is increased by positive covariance between the rate of inflation and the market rate of return, and decreased by negative covariance. However, statistically as the actual covariance has been very small since the latter part of the 19th century, at least in the USA, the measured market price of risk is not affected appreciably by the adjustment for inflation.

The fundamental theorem of asset pricing for unbounded stochastic processes

Abstract: The Fundamental Theorem of Asset Pricing states - roughly speaking - that the absence of arbitrage possibilities for a stochastic process S is equivalent to the existence of an equivalent martingale measure for S. It turns out that it is quite hard to give precise and sharp versions of this theorem in proper generality, if one insists on modifying the concept of "no arbitrage" as little as possible. It was shown in [DS94] that for a locally bounded R^d-valued semi-martingale S the condition of No Free Lunch with Vanishing Risk is equivalent to the existence of an equivalent local martingale measure for the process S. It was asked whether the local boundedness assumption on S may be dropped. In the present paper we show that if we drop in this theorem the local boundedness assumption on S the theorem remains true if we replace the term equivalent local martingale measure by the term equivalent sigma-martingale measure. The concept of sigma-martingales was introduced by Chou and Emery - under the name of "semimartingales de la classe (Sigma_m)". We provide an example which shows that for the validity of the theorem in the non locally bounded case it is indeed necessary to pass to the concept of sigma-martingales. On the other hand, we also observe that for the applications in Mathematical Finance the notion of sigma-martingales provides a natural framework when working with non locally bounded processes S. The duality results which we obtained earlier are also extended to the non locally bounded case. As an application we characterize the hedgeable elements. (author's abstract)

Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market

Abstract: The problem of pricing contingent claims or options from the price dynamics of certain securities is well understood in the context of a complete financial market. This paper studies the same problem in an incomplete market. When the market is incomplete, prices cannot be derived from the absence of arbitrage, since it is not possible to replicate the payoff of a given contingent claim by a controlled portfolio of the basic securities. In this situation, there is a price range for the actual market price of the contingent claim. The maximum and minimum prices are studied using stochastic control methods. The main result of this work is the determination that the maximum price is the smallest price that allows the seller to hedge completely by a controlled portfolio of the basic securities. A similar result is obtained for the minimum price (which corresponds to the purchase price).