Related papers: Market Viability and Completeness for Multinomial …

We consider an incomplete multi-asset binomial market model. We prove that for a wide class of contingent claims the extremal multi-step martingale measure is a power of the corresponding single-step extremal martingale measure. This allows…

In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and…

An explicit formula is derived for the value of weak information in a discrete time model that works for a wide range of utility functions including the logarithmic and power utility. We assume a complete market with a finite number of…

A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for…

We investigate the method of conjugate gradients, exploiting inaccurate matrix-vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring…

We consider the problem of finding a real valued martingale fitting specified marginal distributions. For this to be possible, the marginals must be increasing in the convex order and have constant mean. We show that, under the extra…

We consider a general class of diffusion-based models and show that, even in the absence of an Equivalent Local Martingale Measure, the financial market may still be viable, in the sense that strong forms of arbitrage are excluded and…

We present a range of applications of localisation for constrained transports for pairs of probability measures in order with respect to a lattice cone. These examples comprise irreducible convex paving for martingale transports in…

Mathematical models for financial asset prices which include, for example, stochastic volatility or jumps are incomplete in that derivative securities are generally not replicable by trading in the underlying. In earlier work (2004) the…

In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it the necessary and sufficient conditions of optional Doob decomposition in the discrete case. This…

In this paper the robust utility maximization problem for a market model based on L\'evy processes is analyzed. The interplay between the form of the utility function and the penalization function required to have a well posed problem is…

We are interested in the existence of equivalent martingale measures and the detection of arbitrage opportunities in markets where several multi-asset derivatives are traded simultaneously. More specifically, we consider a financial market…

We develop a unified framework for modeling multiple term structures arising in financial, insurance, and energy markets, adopting an extended Heath-Jarrow-Morton (HJM) approach under the real-world probability. We study market viability…

This paper is the continuation of "Pricing with coherent risk" and deals with further applications of coherent risk measures to problems of finance. First, we study the optimization problem. Three forms of this problem are considered.…

In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by F\"ollmer, Schied (2002). The…

We establish a variant of Monge--Kantorovich duality for a constrained optimal transport problem with a continuum of agents, a finite set of alternatives, and general linear constraints. As an application, we revisit the large-market model…

I study the limit of a large random economy, where a set of consumers invests in financial instruments engineered by banks, in order to optimize their future consumption. This exercise shows that, even in the ideal case of perfect…

The purpose of this article is to describe all possible beliefs of market participants on objective measures under Markovian environments when a risk-neutral measure is given. To achieve this, we employ the Martin integral representation of…

We investigate the supports of extremal martingale measures with pre-specified marginals in a two-period setting. First, we establish in full generality the equivalence between the extremality of a given measure $Q$ and the denseness in…

This paper investigates the optimal choices of financial derivatives to complete a financial market in the framework of stochastic volatility (SV) models. We introduce an efficient and accurate simulation-based method, applicable to…