On the existence of shadow prices for optimal investment with random endowment

On the existence of shadow prices

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 indeed holds in generality has remained elusive so far. In this paper we present a counterexample whic...

On the Existence of Shadow Prices in Finite Discrete Time

A shadow price is a process S̃ lying within the bid/ask prices S, S of a market with proportional transaction costs, such that maximizing expected utility from consumption in the frictionless market with price process S̃ leads to the same maximal utility as in the original market with transaction costs. For finite Ω, this note provides an elementary proof for the existence of such a shadow price.

RANKING DMUS ON THE BENCHMARK LINE WITH EQUAL SHADOW PRICES

Data envelopment analysis (DEA) with considering the best condition for each decision making unit (DMU) assesses the relative efficiency for it and divides a homogenous group of DMUs in to two categories: efficient and inefficient, but traditional DEA models can not rank efficient DMUs. Although some models were introduced for ranking efficient DMUs, Franklin Lio & Hsuan peng (2008), proposed a...

Shadow Prices and Well-Posedness in the Problem of Optimal Investment and Consumption with Transaction Costs

Log-optimal investment in the long run with proportional transaction costs when using shadow prices

We consider a non-consuming agent interested in the maximization of the long-run growth rate of a wealth process investing either in a money market and in one risky asset following a geometric Brownian motion or in futures following an arithmetic Brownian motion. The agent faces proportional transaction costs, and similarly as in [17] where the case of stock trading is considered, we show how t...