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## A proof of the Dalang-Morton-Willinger theorem

Rokhlin, Dmitry B.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
16.74%
We give a new proof of the Dalang-Morton-Willinger theorem, relating the no-arbitrage condition in stochastic securities market models to the existence of an equivalent martingale measure with bounded density for a $d$-dimensional stochastic sequence $(S_n)_{n=0}^N$ of stock prices. Roughly speaking, the proof is reduced to the assertion that under the no-arbitrage condition for N=1 and $S\in L^1$ there exists a strictly positive linear fucntional on $L^1$, which is bounded from above on a special subset of the subspace $K\subset L^1$ of investor's gains.; Comment: 9 pages

## On a Class of Diverse Market Models

Sarantsev, Andrey
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
16.74%
A market model in Stochastic Portfolio Theory is a finite system of strictly positive stochastic processes. Each process represents the capitalization of a certain stock. If at any time no stock dominates almost the entire market, which means that its share of total market capitalization is not very close to one, then the market is called diverse. There are several ways to outperform diverse markets and get an arbitrage opportunity, and this makes these markets interesting. A feature of real-world markets is that stocks with smaller capitalizations have larger drift coefficients. Some models, like the Volatility-Stabilized Model, try to capture this property, but they are not diverse. In an attempt to combine this feature with diversity, we construct a new class of market models. We find simple, easy-to-test sufficient conditions for them to be diverse and other sufficient conditions for them not to be diverse.; Comment: Keywords: Stochastic Portfolio Theory; diverse markets; arbitrage opportunity; Feller's test

## Dynamic Defaultable Term Structure Modelling beyond the Intensity Paradigm

Gehmlich, Frank; Schmidt, Thorsten
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
16.74%
The two main approaches in credit risk are the structural approach pioneered in Merton (1974) and the reduced-form framework proposed in Jarrow & Turnbull (1995) and in Artzner & Delbaen (1995). The goal of this article is to provide a unified view on both approaches. This is achieved by studying reduced-form approaches under weak assumptions. In particular we do not assume the global existence of a default intensity and allow default at fixed or predictable times with positive probability, such as coupon payment dates. In this generalized framework we study dynamic term structures prone to default risk following the forward-rate approach proposed in Heath-Jarrow-Morton (1992). It turns out, that previously considered models lead to arbitrage possibilities when default may happen at a predictable time with positive probability. A suitable generalization of the forward-rate approach contains an additional stochastic integral with atoms at predictable times and necessary and sufficient conditions for a suitable no-arbitrage condition (NAFL) are given. In the view of efficient implementations we develop a new class of affine models which do not satisfy the standard assumption of stochastic continuity. The chosen approach is intimately related to the theory of enlargement of filtrations...

## On Financial Markets Based on Telegraph Processes

Ratanov, Nikita; Melnikov, Alexander
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
16.74%
The paper develops a new class of financial market models. These models are based on generalized telegraph processes: Markov random flows with alternating velocities and jumps occurring when the velocities are switching. While such markets may admit an arbitrage opportunity, the model under consideration is arbitrage-free and complete if directions of jumps in stock prices are in a certain correspondence with their velocity and interest rate behaviour. An analog of the Black-Scholes fundamental differential equation is derived, but, in contrast with the Black-Scholes model, this equation is hyperbolic. Explicit formulas for prices of European options are obtained using perfect and quantile hedging.; Comment: To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.informaworld.com/openurl?genre=journal%26issn=1744-2508) edited by N.H. Bingham and I.V. Evstigneev which will be reprinted as Volume 57 of the IMS Lecture Notes Monograph Series (http://imstat.org/publications/lecnotes.htm)

Brody, Dorje C.; Davis, Mark H. A.; Friedman, Robyn L.; Hughston, Lane P.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
16.74%
An asymmetric information model is introduced for the situation in which there is a small agent who is more susceptible to the flow of information in the market than the general market participant, and who tries to implement strategies based on the additional information. In this model market participants have access to a stream of noisy information concerning the future return of an asset, whereas the informed trader has access to a further information source which is obscured by an additional noise that may be correlated with the market noise. The informed trader uses the extraneous information source to seek statistical arbitrage opportunities, while at the same time accommodating the additional risk. The amount of information available to the general market participant concerning the asset return is measured by the mutual information of the asset price and the associated cash flow. The worth of the additional information source is then measured in terms of the difference of mutual information between the general market participant and the informed trader. This difference is shown to be nonnegative when the signal-to-noise ratio of the information flow is known in advance. Explicit trading strategies leading to statistical arbitrage opportunities...

## Monotonicity of the collateralized debt obligations term structure model

Barski, Michał
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
16.74%
The problem of existence of arbitrage free and monotone CDO term structure models is studied. Conditions for positivity and monotonicity of the corresponding Heath-Jarrow-Morton-Musiela equation for the $x$-forward rates with the use of the Milian type result are formulated. Two state spaces are taken into account - of square integrable functions and a Sobolev space. For the first the regularity results concerning pointwise monotonicity are proven. Arbitrage free and monotone models are characterized in terms of the volatility of the model and characteristics of the driving L\'evy process.; Comment: 28 pages

## On the Stickiness Property

Bayraktar, Erhan; Sayit, Hasanjan
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
16.74%
In [2] the notion of stickiness for stochastic processes was introduced. It was also shown that stickiness implies absense of arbitrage in a market with proportional transaction costs. In this paper, we investigate the notion of stickiness further. In particular, we give examples of processes that are not semimartingales but are sticky.; Comment: Key words: Transaction costs. No Arbitrage. Sticky processes. Time change

## Physics of Finance

Ilinski, Kirill
Tipo: Artigo de Revista Científica