We prove a general version of the super-replication theorem, which applies to Kabanov’s model of foreign exchange markets under proportional transaction costs. The market is described by a matrix-valued càdlàg bid-ask process $$(\Pi_t)_{t\in [0,T]}$$ evolving in continuous time. We propose a...

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 {\em shadow market} that yields the same optimal strategy and utility. However, the question of whether or not...

We present an optimal investment theorem for a currency exchange model with random and possibly discontinuous proportional transaction costs. The investor’s preferences are represented by a smooth, multivariate utility function, allowing for simultaneous consumption of any prescribed selection...

We consider a mean-variance hedging (MVH) problem for an arbitrage-free large financial market, that is, a financial market with countably many risky assets modelled by a sequence of continuous semimartingales. By using the stochastic integration theory for a sequence of semimartingales...

We consider an equilibrium model á la Kyle-Back for a defaultable claim issued by a given firm. In such a market the insider observes \emph{continuously in time} the value of firm, which is unobservable by the market maker. Using the construction of a dynamic Bessel bridge of dimension $3$ in...

In this paper, we study the optimal portfolio selection problem of weakly informed traders in the sense of Baudoin \cite{Baudoin_2002}. Instead of considering only expected utility maximizers, we also take into consideration different preference paradigms. In particular, we analyze a...

We develop a structural risk-neutral model for energy market modifying along several directions the approach introduced in Aïd et al. In particular, a scarcity function is introduced to allow important deviations of the spot price from the marginal fuel price, producing price spikes. We focus...

We present an optimal investment theorem for a currency exchange model with random and possibly discontinuous proportional transaction costs. The investor’s preferences are represented by a multivariate utility function, allowing for simultaneous consumption of any prescribed selection of the...

We consider a non necessarily complete financial market with one bond and one risky asset, whose price process is modelled by a suitably integrable, strictly positive, càdlàg process $S$ over $[0, T]$. Every option price is defined as the conditional expectation under a given equivalent (true)...

In this paper we deal with a utility maximization problem at finite horizon on a continuous-time market with conical (and time varying) constraints (particularly suited to model a currency market with proportional transaction costs). In particular, we extend the results in Campi and Owen (2011)...