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...

We study, in the framework of Back [Rev. Financial Stud. 5(3), 387–409 (1992)], an equilibrium model for the pricing of a defaultable zero coupon bond issued by a firm. The market consists of a risk-neutral informed agent, noise traders, and a market maker who sets the price using the total...

Unlike in structural and reduced-form models, we use equity as a liquid and observable primitive to analytically value corporate bonds and credit default swaps. Restrictive assumptions on the firm’s capital structure are avoided. Default is parsimoniously represented by equity value hitting...

In commodity markets, the convergence of futures towards spot prices as the time to maturity of the contracts goes to zero is usually justified by no-arbitrage arguments. In this paper we propose an alternative approach, that relies on the expected profit maximization problem of an agent...

In this article, we characterize efficient portfolios, i.e. portfolios which are optimal for at least one rational agent, in a very general financial market model of foreign currencies with proportional transaction costs. In our setting, transaction costs may be random, time dependent, have...

In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time...

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...

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...