3,334 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
Optimal Investment with Random Endowments and Transaction Costs: Duality Theory and Shadow Prices
This paper studies the utility maximization on the terminal wealth with
random endowments and proportional transaction costs. To deal with unbounded
random payoffs from some illiquid claims, we propose to work with the
acceptable portfolios defined via the consistent price system (CPS) such that
the liquidation value processes stay above some stochastic thresholds. In the
market consisting of one riskless bond and one risky asset, we obtain a type of
super-hedging result. Based on this characterization of the primal space, the
existence and uniqueness of the optimal solution for the utility maximization
problem are established using the duality approach. As an important application
of the duality theorem, we provide some sufficient conditions for the existence
of a shadow price process with random endowments in a generalized form as well
as in the usual sense using acceptable portfolios.Comment: Final version. To appear in Mathematics and Financial Economics.
Keywords: Proportional Transaction Costs, Unbounded Random Endowments,
Acceptable Portfolios, Super-hedging Theorem, Utility Maximization, Shadow
Prices, Convex Dualit
Portfolio optimisation beyond semimartingales: shadow prices and fractional Brownian motion
While absence of arbitrage in frictionless financial markets requires price
processes to be semimartingales, non-semimartingales can be used to model
prices in an arbitrage-free way, if proportional transaction costs are taken
into account. In this paper, we show, for a class of price processes which are
not necessarily semimartingales, the existence of an optimal trading strategy
for utility maximisation under transaction costs by establishing the existence
of a so-called shadow price. This is a semimartingale price process, taking
values in the bid ask spread, such that frictionless trading for that price
process leads to the same optimal strategy and utility as the original problem
under transaction costs. Our results combine arguments from convex duality with
the stickiness condition introduced by P. Guasoni. They apply in particular to
exponential utility and geometric fractional Brownian motion. In this case, the
shadow price is an Ito process. As a consequence we obtain a rather surprising
result on the pathwise behaviour of fractional Brownian motion: the
trajectories may touch an Ito process in a one-sided manner without reflection.Comment: To appear in Annals of Applied Probability. We would like to thank
Junjian Yang for careful reading of the manuscript and pointing out a mistake
in an earlier versio
Linear vector optimization and European option pricing under proportional transaction costs
A method for pricing and superhedging European options under proportional
transaction costs based on linear vector optimisation and geometric duality
developed by Lohne & Rudloff (2014) is compared to a special case of the
algorithms for American type derivatives due to Roux & Zastawniak (2014). An
equivalence between these two approaches is established by means of a general
result linking the support function of the upper image of a linear vector
optimisation problem with the lower image of the dual linear optimisation
problem
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