Related papers: Shadow prices, fractional Brownian motion, and por…

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 a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process,…

In this paper, we consider a num\'eraire-based utility maximization problem under constant proportional transaction costs and random endowment. Assuming that the agent cannot short sell assets and is endowed with a strictly positive…

For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a "shadow price", i.e., a least favorable frictionless market extension leading to the same optimal strategy and utility. By means of…

In frictionless markets, utility maximization problems are typically solved either by stochastic control or by martingale methods. Beginning with the seminal paper of Davis and Norman [Math. Oper. Res. 15 (1990) 676--713], stochastic…

For portfolio optimisation under proportional transaction costs, we provide a duality theory for general cadlag price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised…

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…

We consider the problem of optimizing the expected logarithmic utility of the value of a portfolio in a binomial model with proportional transaction costs with a long time horizon. By duality methods, we can find expressions for the…

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…

Shadow prices simplify the derivation of optimal trading strategies in markets with transaction costs by transferring optimization into a more tractable, frictionless market. This paper establishes that a na\"ive shadow price Ansatz for…

A standing assumption in the literature on proportional transaction costs is efficient friction. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation, as they usually appear in frictionless…

We consider conditional-mean hedging in a fractional Black-Scholes pricing model in the presence of proportional transaction costs. We develop an explicit formula for the conditional-mean hedging portfolio in terms of the recently…

A shadow price is a process lying within the bid/ask prices of a market with proportional transaction costs, such that maximizing expected utility from consumption in the frictionless market with this price process leads to the same maximal…

We survey some new progress on the pricing models driven by fractional Brownian motion \cb{or} mixed fractional Brownian motion. In particular, we give results on arbitrage opportunities, hedging, and option pricing in these models. We…

We consider the problem of maximizing expected power utility from consumption over an infinite horizon in the Black-Scholes model with proportional transaction costs, as studied in Shreve and Soner [Ann. Appl. Probab. 4 (1994) 609-692].…

To any utility maximization problem under transaction costs one can assign a frictionless model with a price process $S^*$, lying in the bid/ask price interval $[\underline S, \bar{S}]$. Such process $S^*$ is called a \emph{shadow price} if…

We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a num\'eraire-based semi-static utility maximization problem with an exponential utility preference. The randomization…

This paper discusses the num\'eraire-based utility maximization problem in markets with proportional transaction costs. In particular, the investor is required to liquidate all her position in stock at the terminal time. We first observe…

We consider the maximization of the long-term growth rate in the Black-Scholes model under proportional transaction costs as in Taksar, Klass and Assaf [Math. Oper. Res. 13, 1988]. Similarly as in Kallsen and Muhle-Karbe [Ann. Appl.…

We consider the Brownian market model and the problem of expected utility maximization of terminal wealth. We, specifically, examine the problem of maximizing the utility of terminal wealth under the presence of transaction costs of a…