116 research outputs found
General indifference pricing with small transaction costs
We study the utility indifference price of a European option in the context
of small transaction costs. Considering the general setup allowing consumption
and a general utility function at final time T, we obtain an asymptotic
expansion of the utility indifference price as a function of the asymptotic
expansions of the utility maximization problems with and without the European
contingent claim. We use the tools developed in [54] and [48] based on
homogenization and viscosity solutions to characterize these expansions.
Finally we study more precisely the example of exponential utilities, in
particular recovering under weaker assumptions the results of [6].Comment: 43 page
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
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
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