Kreps, martingales and arbitrage in multiperiod securities markets, j. A general theory of asset valuation under diffusion state. Preferences strictly monotone, convex, lower semicontinuous 3. Arbitrage in continuous complete markets volume 34 issue 3 eckhard platen. It emphasizes application to unique pricing in arbitragefree model, the derivation of hedge ratios and the pde when price ratios are diffusions, explicit representations in the multivariate poisson model, and the role played by homogeneity. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Martingale theory in securities and options markets with their work martingales and arbitrage in multiperiod securities markets. Arbitrage in continuous complete markets advances in. Kreps graduate school of business, stanford university, stanford, california 94305. Shiller shows that the volatility of longterm interest rates is greater than predicted. Arbitrage and financial decision making4 lecture notes ii. A price system that admits no free lunches is related to martingales when agents have rational expectations. Kreps, 1978 we consider in this paper some foundational issues that arise in conjunction with the arbitrage theory of option pricing.
Martingales and arbitrage in multiperiod securities markets,journal of economic theory, 20, 381408. Jet journal of economic theory vol 20, issue 3, pages. Martingale and arbitrage in multiperiod securities markets. Kreps, martingales and arbitrage in multiperiod securities markets, journal of economic theory 20 1979, 381408. John michael harrison born 1944 is an american researcher, known for his contributions to the theory of operations research, in particular stochastic networks and financial engineering. The harrisonpliska story and a little bit more stanley r pliska professor emeritus. Pliska, martingales and stochastic integrals in the theory of continuous trading, stochastic processes and their applications 11 1981, 215260.
Martingales, arbitrage, and portfolio choice springerlink. Also a link among all equivalent martingale measures under restricted information market is given. Martingale measures in the market with restricted information. This paper considers the problem of the market with restricted information. Kreps graduate school of business, stanford university, stanford, california 94305 received may 24, 1978. Securities markets, diffusion state processes, and arbitragefree shadow prices volume 29 issue 2 john heaney, geoffrey poitras. Williams american mathematical society providence,rhode island graduate studies in mathematics volume 72. Sorry, we are unable to provide the full text but you may find it at the following locations. Nyu stern financial theory iv continuoustime finance. Arbitrage and equilibrium in economies with in nitely many commodities, journal of mathematical economics 8, 1535. By assuming that the consumption space is separable and thereby extending a. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. This is an extension of a result by harrison and kreps 1979.
Martingales and stochastic integrals in the theory of continuous trading. Harrison and kreps publish martingales and arbitrage in multiperiod securities markets. Purchasing and selling the same security at the same time in different markets to take advantage of a price difference between the two separate markets. This is a brief and informal presentation, for mathematicians not familiar with the topic, of the connections in finance theory between the notions of arbitrage and martingales, with applications to the pricing of securities and to portfolio choice. Martingales and arbitrage in multiperiod securities markets, journal of economic theory, 203, pp. We consider in this paper some foundational issues that arise in conjunction with the arbitrage theory of option pricing. Free snacks and cheap thrills, economic theory 16, 5161. This question is important in a widely studied problem which arises in the theory of finite period securities markets with one riskless bond and a finite number of risky stocks. Martingales and arbitrage in multiperiod securities markets. Coherentprice systems and uncertaintyneutral valuation. We characterize those vectorvalued stochastic processes with a finite index set and defined on an arbitrarystochasic base which can become a martingale under an equivalent change of measure. Journal of economic theory 20, 381408 1979 martingales and arbitrage in multiperiod securities markets j. Stiglitz show that it is impossible for a market to be perfectly informationally efficient.
Pricing of options in emerging financial markets using. Fractional martingales and characterization of the fractional brownian motion hu, yaozhong, nualart, david, and song, jian, the annals of probability, 2009 euclid. Martingales and arbitrage in multiperiod securities markets an aggregation theorem for securities markets introduction to securities trading and markets. Kreps, 1979, martingales and arbitrage in multiperiod securities markets, journal of economic theory, 20, 381408.
The concept of a multiperiod market model is a natural extension of the notion of a singleperiod market model with only two dates. Pliska, 1981, martingales and stochastic integrals in the theory of continuous trading, stochastic processes and. Martingale pricing theory in discretetime and discrete. He has authored two books and nearly 90 journal articles. Martingales and arbitrage in multiperiod securities markets, journal. Thatis,attime1whenagentslongandshortpositionsoflonglivedsecuritiesneedto be settled, they will knowhow many units of consumptiongood to which theyare entitled or obligated. By constructing a restricted information market model, the explicit relation of arbitrage and the minimal martingale measure between two different information markets are discussed. Martingales and arbitrage in multiperiod securities markets by j. This is a short version of the paper of exchange options 2007, concentrating on the principle of numeraire invariance. Pliska, 1981, martingales and stochastic integrals in the theory.
In this theory, initiated by black and scholes 4, one takes as given the price dynamics of certain securities such as stocks and bonds. Martingales and arbitrage in multiperiod securities. The equivalence will be established under quite weak assumptions since there are no conditions on the set of trading dates it may be finite or countable, with bounded or unbounded horizon, etc. Existence of optimal demand, or viability of the price system 6. Securities markets, diffusion state processes, and. Abstract we model multiperiod securities markets with di. Arbitrage, martingales, and stochastic discount factors 1. Martingale pricing theory in discretetime and discretespace models 3 note that the date t 0 cost of the three securities has nothing to do with whether or not a claim is attainable. For a securities market model as above, an equivalent martingale measure is a probability measure p on q, f having three properties. This paper addresses the equivalence between the absence of arbitrage and the existence of equivalent martingale measures. Martingales and arbitrage in securities markets with transaction costs.
1183 485 286 791 603 1043 814 588 638 835 871 745 1257 238 841 238 770 7 655 1156 1467 17 1158 1541 790 157 57 1380 762 847 1083 1261 1274 439 1095 1074 1033