Arbitrage and pricing in a general model with flows

Jan Palczewski¹

¹ Institute of Mathematics Polish Academy of Sciences P.O. Box 21 00-956 Warszawa, Poland

Applicationes Mathematicae, Tome 30 (2003) no. 4, pp. 413-440

Résumé

We study a fundamental issue in the theory of modeling of financial markets. We consider a model where any investment opportunity is described by its cash flows. We allow for a finite number of transactions in a finite time horizon. Each transaction is held at a random moment. This places our model closer to the real world situation than discrete-time or continuous-time models. Moreover, our model creates a general framework to consider markets with different types of imperfection: proportional transaction costs, frictions on the numeraire, etc.We develop an analog of the fundamental theorem of asset pricing. We show that lack of arbitrage is essentially equivalent to existence of a Lipschitz continuous discount process such that the expected value of discounted cash flows of any investment is non-positive. We address the question of contingent claim pricing and hedging.

Détail

DOI : 10.4064/am30-4-4

Keywords: study fundamental issue theory modeling financial markets consider model where investment opportunity described its cash flows allow finite number transactions finite time horizon each transaction held random moment places model closer real world situation discrete time continuous time models moreover model creates general framework consider markets different types imperfection proportional transaction costs frictions numeraire etc develop analog fundamental theorem asset pricing lack arbitrage essentially equivalent existence lipschitz continuous discount process expected value discounted cash flows investment non positive address question contingent claim pricing hedging