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Arbitrage and pricing in a general model with flows

100%
Palczewski J.
Applicationes Mathematicae
|
2003
|
tom 30
|
nr 4
413-440
EN
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.
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Growth-optimal portfolios under transaction costs

63%
Palczewski J., Stettner Ł.
Applicationes Mathematicae
|
2008
|
tom 35
|
nr 1
1-31
EN
This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depends on an external process of economic factors. There are transaction costs with a structure that covers, in particular, the case of fixed plus proportional costs. We prove that there exists a self-financing trading strategy maximizing the average growth rate of the portfolio wealth. We show that this strategy has a Markovian form. Our result is obtained by large deviations estimates on empirical measures of the price process and by a generalization of the vanishing discount method to discontinuous transition operators.
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