162 research outputs found
Hedging, arbitrage and optimality with superlinear frictions
In a continuous-time model with multiple assets described by c\`{a}dl\`{a}g
processes, this paper characterizes superhedging prices, absence of arbitrage,
and utility maximizing strategies, under general frictions that make execution
prices arbitrarily unfavorable for high trading intensity. Such frictions
induce a duality between feasible trading strategies and shadow execution
prices with a martingale measure. Utility maximizing strategies exist even if
arbitrage is present, because it is not scalable at will.Comment: Published at http://dx.doi.org/10.1214/14-AAP1043 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Sticky processes, local and true martingales
We prove that for a so-called sticky process there exists an equivalent
probability and a -martingale that is arbitrarily close to
in norm. For continuous , can be chosen arbitrarily
close to in supremum norm. In the case where is a local martingale we
may choose arbitrarily close to the original probability in the total
variation norm. We provide examples to illustrate the power of our results and
present applications in mathematical finance
Optimal investment under behavioural criteria -- a dual approach
We consider a discrete-time, generically incomplete market model and a
behavioural investor with power-like utility and distortion functions. The
existence of optimal strategies in this setting has been shown in a previous
paper under certain conditions on the parameters of these power functions.
In the present paper we prove the existence of optimal strategies under a
different set of conditions on the parameters, identical to the ones which were
shown to be necessary and sufficient in the Black-Scholes model.
Although there exists no natural dual problem for optimisation under
behavioural criteria (due to the lack of concavity), we will rely on techniques
based on the usual duality between attainable contingent claims and equivalent
martingale measures.Comment: Forthcoming in Banach Center Publications. Some errors have been
corrected, in particular in Assumption 2.3
Hiding a drift
In this article we consider a Brownian motion with drift of the form
dS_t=\mu_t dt+dB_t\qquadfor t\ge0, with a specific nontrivial
, predictable with respect to , the natural
filtration of the Brownian motion . We construct a process
, also predictable with respect to , such that
is a Brownian motion in its own filtration.
Furthermore, for any , we refine this construction such that the
drift only takes values in , for
fixed .Comment: Published in at http://dx.doi.org/10.1214/09-AOP469 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Asymptotic Exponential Arbitrage and Utility-based Asymptotic Arbitrage in Markovian Models of Financial Markets
Consider a discrete-time infinite horizon financial market model in which the
logarithm of the stock price is a time discretization of a stochastic
differential equation. Under conditions different from those given in a
previous paper of ours, we prove the existence of investment opportunities
producing an exponentially growing profit with probability tending to
geometrically fast. This is achieved using ergodic results on Markov chains and
tools of large deviations theory.
Furthermore, we discuss asymptotic arbitrage in the expected utility sense
and its relationship to the first part of the paper.Comment: Forthcoming in Acta Applicandae Mathematica
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