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## Large Financial Markets and Asymptotic Arbitrage with Small Transaction Costs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/11/2012
Português

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We give characterizations of asymptotic arbitrage of the first and second
kind and of strong asymptotic arbitrage for large financial markets with small
proportional transaction costs $\la_n$ on market $n$ in terms of contiguity
properties of sequences of equivalent probability measures induced by
$\la_n$--consistent price systems. These results are analogous to the
frictionless case. Our setting is simple, each market $n$ contains two assets
with continuous price processes. The proofs use quantitative versions of the
Halmos--Savage Theorem and a monotone convergence result of nonnegative local
martingales. Moreover, we present an example admitting a strong asymptotic
arbitrage without transaction costs; but with transaction costs $\la_n>0$ on
market $n$ ($\la_n\to0$ not too fast) there does not exist any form of
asymptotic arbitrage.

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## Strong asymptotic arbitrage in the large fractional binary market

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We study, from the perspective of large financial markets, the asymptotic
arbitrage opportunities in a sequence of binary markets approximating the
fractional Black-Scholes model. This approximating sequence was introduced by
Sottinen and named fractional binary market. The large financial market under
consideration does not satisfy the standard assumptions of the theory of
asymptotic arbitrage. For this reason, we follow a constructive approach to
show first that a strong type of asymptotic arbitrage exists in the large
market without transaction costs. Indeed, with the help of an appropriate
version of the law of large numbers and a stopping time procedure, we construct
a sequence of self-financing strategies, which leads to the desired result.
Next, we introduce, in each small market, proportional transaction costs, and
we construct, following a similar argument, a sequence of self-financing
strategies providing a strong asymptotic arbitrage when the transaction costs
converge fast enough to 0.; Comment: 21 pages

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## Geometric Arbitrage and Spectral Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/09/2015
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Geometric Arbitrage Theory reformulates a generic asset model possibly
allowing for arbitrage by packaging all assets and their forwards dynamics into
a stochastic principal fibre bundle, with a connection whose parallel transport
encodes discounting and portfolio rebalancing, and whose curvature measures, in
this geometric language, the "instantaneous arbitrage capability" generated by
the market itself. The cashflow bundle is the vector bundle associated to this
stochastic principal fibre bundle for the natural choice of the vector space
fibre. The cashflow bundle carries a stochastic covariant differentiation
induced by the connection on the principal fibre bundle. The link between
arbitrage theory and spectral theory of the connection Laplacian on the vector
bundle is given by the zero eigenspace resulting in a parametrization of all
risk neutral measures equivalent to the statistical one. This indicates that a
market satisfies the no-free-lunch-with vanishing-risk condition if it is only
if $0$ is in the spectrum.; Comment: arXiv admin note: substantial text overlap with arXiv:1406.6805,
arXiv:0910.1671

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## Arbitrage and Hedging in a non probabilistic framework

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/03/2011
Português

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The paper studies the concepts of hedging and arbitrage in a non
probabilistic framework. It provides conditions for non probabilistic arbitrage
based on the topological structure of the trajectory space and makes
connections with the usual notion of arbitrage. Several examples illustrate the
non probabilistic arbitrage as well perfect replication of options under
continuous and discontinuous trajectories, the results can then be applied in
probabilistic models path by path. The approach is related to recent financial
models that go beyond semimartingales, we remark on some of these connections
and provide applications of our results to some of these models.

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## Non-arbitrage for Informational Discrete Time Market Models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/07/2014
Português

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This paper focuses on the stability of the non-arbitrage condition in
discrete time market models when some unknown information $\tau$ is
partially/fully incorporated into the market. Our main conclusions are twofold.
On the one hand, for a fixed market $S$, we prove that the non-arbitrage
condition is preserved under a mild condition. On the other hand, we give the
necessary and sufficient equivalent conditions on the unknown information
$\tau$ to ensure the validity of the non-arbitrage condition for any market.
Two concrete examples are presented to illustrate the importance of these
conditions, where we calculate explicitly the arbitrage opportunities when they
exist.; Comment: 22 pages

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## Arbitrage Bounds for Prices of Weighted Variance Swaps

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We develop robust pricing and hedging of a weighted variance swap when market
prices for a finite number of co--maturing put options are given. We assume the
given prices do not admit arbitrage and deduce no-arbitrage bounds on the
weighted variance swap along with super- and sub- replicating strategies which
enforce them. We find that market quotes for variance swaps are surprisingly
close to the model-free lower bounds we determine. We solve the problem by
transforming it into an analogous question for a European option with a convex
payoff. The lower bound becomes a problem in semi-infinite linear programming
which we solve in detail. The upper bound is explicit.
We work in a model-independent and probability-free setup. In particular we
use and extend F\"ollmer's pathwise stochastic calculus. Appropriate notions of
arbitrage and admissibility are introduced. This allows us to establish the
usual hedging relation between the variance swap and the 'log contract' and
similar connections for weighted variance swaps. Our results take form of a
FTAP: we show that the absence of (weak) arbitrage is equivalent to the
existence of a classical model which reproduces the observed prices via
risk-neutral expectations of discounted payoffs.; Comment: 25 pages...

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## Spontaneous symmetry breaking of arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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#Quantitative Finance - General Finance#Condensed Matter - Statistical Mechanics#Quantitative Finance - Portfolio Management

We introduce the concept of spontaneous symmetry breaking to arbitrage
modeling. In the model, the arbitrage strategy is considered as being in the
symmetry breaking phase and the phase transition between arbitrage mode and
no-arbitrage mode is triggered by a control parameter. We estimate the control
parameter for momentum strategy with real historical data. The momentum
strategy aided by symmetry breaking shows stronger performance and has a better
risk measure than the naive momentum strategy in U.S. and South Korean markets.; Comment: 23 pages, 6 figures; Published version

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## No Arbitrage Conditions For Simple Trading Strategies

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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Strict local martingales may admit arbitrage opportunities with respect to
the class of simple trading strategies. (Since there is no possibility of using
doubling strategies in this framework, the losses are not assumed to be bounded
from below.) We show that for a class of non-negative strict local martingales,
the strong Markov property implies the no arbitrage property with respect to
the class of simple trading strategies. This result can be seen as a
generalization of a similar result on three dimensional Bessel process in [3].
We also pro- vide no arbitrage conditions for stochastic processes within the
class of simple trading strategies with shortsale restriction.; Comment: Keywords: Simple trading strategies. Arbitrage. Sticky processes.
Short-Sales Restrictions

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## Weak and strong no-arbitrage conditions for continuous financial markets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We propose a unified analysis of a whole spectrum of no-arbitrage conditions
for financial market models based on continuous semimartingales. In particular,
we focus on no-arbitrage conditions weaker than the classical notions of No
Arbitrage and No Free Lunch with Vanishing Risk. We provide a complete
characterisation of the considered no-arbitrage conditions, linking their
validity to the characteristics of the discounted asset price process and to
the existence and the properties of (weak) martingale deflators, and review
classical as well as recent results.; Comment: 28 pages

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