For utility maximization problems under proportional transaction costs, it has been observed that the original market with transaction costs can sometimes be replaced by a frictionless shadow market that yields the same optimal strategy and utility. However, the question of whether or not this...

<title>Abstract</title> We consider the performance of non-optimal hedging strategies in exponential Lévy models. Given that both the payoff of the contingent claim and the hedging strategy admit suitable integral representations, we use the Laplace transform approach of Hubalek <italic>et al</italic>. [<italic>Ann. Appl. Probab.</italic>,...

We consider local martingales of exponential form or , where X denotes one component of a multivariate affine process. We give a weak sufficient criterion for M to be a true martingale. As a first application, we derive a simple sufficient condition for absolute continuity of the laws of two...

A shadow price is a process <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\widetilde{S}}$$</EquationSource> </InlineEquation> lying within the bid/ask prices <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${\underline{S},\overline{S}}$$</EquationSource> </InlineEquation> of a market with proportional transaction costs, such that maximizing expected utility from consumption in the frictionless market with price process <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$${\widetilde{S}}$$</EquationSource> </InlineEquation> leads...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

We consider the classical problem of maximizing expected utility from terminal wealth. With the help of a martingale criterion explicit solutions are derived for power utility in a number of affine stochastic volatility models.

A shadow price is a process $${\widetilde{S}}$$ lying within the bid/ask prices $${\underline{S},\overline{S}}$$ of a market with proportional transaction costs, such that maximizing expected utility from consumption in the frictionless market with price process $${\widetilde{S}}$$ leads to the...

We investigate the general structure of optimal investment and consumption with small proportional transaction costs. For a safe asset and a risky asset with general continuous dynamics, traded with random and time-varying but small transaction costs, we derive simple formal asymptotics for the...

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...