Leland’s approach to the hedging of derivatives under proportional transaction costs is based on an approximate replication of the European-type contingent claim V T using the classical Black–Scholes formula with a suitably enlarged volatility. The formal mathematical framework is a scheme...

In contrast with the classical models of frictionless financial markets, market models with proportional transaction costs, even satisfying usual no-arbitrage properties, may admit arbitrage opportunities of the second kind. This means that there are self-financing portfolios with initial...

In the first part of the paper, we study concepts of supremum and maximum as subsets of a topological space X endowed by preference relations. Several rather general existence theorems are obtained for the case where the preferences are defined by countable semicontinuous multi-utility...

We consider a multi-asset continuous-time model of a financial market with transaction costs and prove that, for a strongly risk-averse investor, the reservation price of a contingent claim approaches the super-replication price increased by the liquidation value of the initial endowment.

In contrast with the classical models of frictionless financial markets, market models with proportional transaction costs, even satisfying usual no-arbitrage properties, may admit arbitrage opportunities of the second kind. This means that there are self-financing portfolios with initial...

Inspired by the theory of financial markets with transaction costs, we study a concept of essential supremum in the framework where a random partial order in View the MathML source is lifted to the space View the MathML source of d-dimensional random variables. In contrast to the classical...