We remove the technical assumption $\gamma>0$ imposed by Dai et. al. who consider the optimal investment and consumption decision of a CRRA investor facing proportional transaction costs and finite time horizon. As a by-product, we obtain an estimate on the optimal consumption

In frictionless markets, the absence of arbitrage opportunities is equivalent to the existence of a martingale process evolving in the ray R_ S where S is the d-dimensional price process (whose first component is the numeraire). With transaction costs, absence of arbitrage opportunities is...

We study the Leland model for hedging portfolios in the presence of a constant proportional transaction costs coefficient. The modified Leland's strategy defined in [2], contrarily to the classical one, ensures the asymptotic replication of a large class of payoff. In this setting, we prove a...

In 1985 Leland suggested an approach to price contingent claims under proportional transaction costs. Its main idea is to use the classical Black–Scholes formula with a suitably adjusted volatility for a periodical revision of the portfolio whose terminal value approximates the pay-off....

Leland's approach to the hedging of derivatives under proportional transaction costs is based on an approximate replication of the European-type contingent claim VT using the classical Black Scholes formulae with a suitably enlarged volatility. The formal mathematical framework is a scheme of...

We consider the problem of tracking the optimal allocation between a risky and a risk-free asset when the expected return is stochastic and trading incurs transaction costs. The rebalancing policy optimises the tradeoff between the opportunity cost of holding a suboptimal portfolio and the...

Frontier markets, sometimes referred to as “emerging emerging markets,” have high transaction costs so investors who rebalance their portfolios monthly do not receive diversification benefits. However, diversification gains can be achieved by investors rebalancing every three months or...

The transaction costs applied by various european online brokers are now given by piecewise affine functions. So it is interesting to analyze the behaviour of any portfolio in this market context. Our purpose in this work is to determine the expected value and variance of a portfolio return...

This paper concerns continuous-time optimal investment and consumption decision of a CRRA investor who faces proportional transaction costs and finite time horizon. In the no consumption case, it has been studied by Liu and Loewenstein (2002) and Dai and Yi (2006). Mathematically, it is a...