74 research outputs found
Portfolio Optimization under Small Transaction Costs: a Convex Duality Approach
We consider an investor with constant absolute risk aversion who trades a
risky asset with general Ito dynamics, in the presence of small proportional
transaction costs. Kallsen and Muhle-Karbe (2012) formally derived the
leading-order optimal trading policy and the associated welfare impact of
transaction costs. In the present paper, we carry out a convex duality approach
facilitated by the concept of shadow price processes in order to verify the
main results of Kallsen and Muhle-Karbe under well-defined regularity
conditions
On the Structure of General Mean-Variance Hedging Strategies
We provide a new characterization of mean-variance hedging strategies in a
general semimartingale market. The key point is the introduction of a new
probability measure which turns the dynamic asset allocation
problem into a myopic one. The minimal martingale measure relative to
coincides with the variance-optimal martingale measure relative to
the original probability measure .Comment: Published at http://dx.doi.org/10.1214/009117906000000872 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Option Pricing and Hedging with Small Transaction Costs
An investor with constant absolute risk aversion trades a risky asset with
general It\^o-dynamics, in the presence of small proportional transaction
costs. In this setting, we formally derive a leading-order optimal trading
policy and the associated welfare, expressed in terms of the local dynamics of
the frictionless optimizer. By applying these results in the presence of a
random endowment, we obtain asymptotic formulas for utility indifference prices
and hedging strategies in the presence of small transaction costs.Comment: 20 pages, to appear in "Mathematical Finance
High-Resilience Limits of Block-Shaped Order Books
We show that wealth processes in the block-shaped order book model of
Obizhaeva/Wang converge to their counterparts in the reduced-form model
proposed by Almgren/Chriss, as the resilience of the order book tends to
infinity. As an application of this limit theorem, we explain how to reduce
portfolio choice in highly-resilient Obizhaeva/Wang models to the corresponding
problem in an Almgren/Chriss setup with small quadratic trading costs.Comment: 12 page
Variance-optimal hedging for processes with stationary independent increments
We determine the variance-optimal hedge when the logarithm of the underlying
price follows a process with stationary independent increments in discrete or
continuous time. Although the general solution to this problem is known as
backward recursion or backward stochastic differential equation, we show that
for this class of processes the optimal endowment and strategy can be expressed
more explicitly. The corresponding formulas involve the moment, respectively,
cumulant generating function of the underlying process and a Laplace- or
Fourier-type representation of the contingent claim. An example illustrates
that our formulas are fast and easy to evaluate numerically.Comment: Published at http://dx.doi.org/10.1214/105051606000000178 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Asymptotic Power Utility-Based Pricing and Hedging
Kramkov and Sirbu (2006, 2007) have shown that first-order approximations of
power utility-based prices and hedging strategies can be computed by solving a
mean-variance hedging problem under a specific equivalent martingale measure
and relative to a suitable numeraire. In order to avoid the introduction of an
additional state variable necessitated by the change of numeraire, we propose
an alternative representation in terms of the original numeraire. More
specifically, we characterize the relevant quantities using semimartingale
characteristics similarly as in Cerny and Kallsen (2007) for mean-variance
hedging. These results are illustrated by applying them to exponential L\'evy
processes and stochastic volatility models of Barndorff-Nielsen and Shephard
type.Comment: 32 pages, 4 figures, to appear in "Mathematics and Financial
Economics
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