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Financial models are studied where each asset may potentially lose value relative to any other. Conditioning on non-devaluation, each asset can serve as proper num\'eraire and classical valuation rules can be formulated. It is shown when…
We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their…
We consider the problem of option pricing and hedging when stock returns are correlated in time. Within a quadratic-risk minimisation scheme, we obtain a general formula, valid for weakly correlated non-Gaussian processes. We show that for…
We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for large financial markets with small proportional transaction costs $\la_n$ on market $n$ in terms of contiguity properties…
A common assumption in financial engineering is that the market price for any derivative coincides with an objectively defined risk-neutral price - a plausible assumption only if traders collectively possess objective knowledge about the…
In both finance and economics, quantitative models are usually studied as isolated mathematical objects --- most often defined by very strong simplifying assumptions concerning rationality, efficiency and the existence of disequilibrium…
We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability or excessive tail-risk seeking behaviour if the market admits statistical arbitrage opportunities which we term…
In this paper, we study the pricing of contracts in fixed income markets under volatility uncertainty in the sense of Knightian uncertainty or model uncertainty. The starting point is an arbitrage-free bond market under volatility…
This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are…
This work considers a stochastic model in which the uncertainty is driven by a multidimensional Brownian motion. The market price of risk process makes the transition between real world probability measure and risk neutral probability…
We study arbitrage opportunities, market viability and utility maximization in market models with an insider. Assuming that an economic agent possesses from the beginning an additional information in the form of a random variable G, which…
We present a new framework for Hermite fractional financial markets, generalizing the fractional Brownian motion and fractional Rosenblatt markets. Considering pure and mixed Hermite markets, we introduce a strategy-specific arbitrage tax…
We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional…
We consider the classical problem of building an arbitrage-free implied volatility surface from bid-ask quotes. We design a fast numerical procedure, for which we prove the convergence, based on the Sinkhorn algorithm that has been recently…
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in…
We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in discrete time. In particular, we prove a Fundamental Theorem of Asset Pricing and a Superhedging Theorem,…
In general it is not clear which kind of information is supposed to be used for calculating the fair value of a contingent claim. Even if the information is specified, it is not guaranteed that the fair value is uniquely determined by the…
In an incomplete Brownian-motion market setting, we propose a convex monotonic pricing functional for nonattainable bounded contingent claims which is compatible with prices for attainable claims. The pricing functional is defined as the…
We study the pricing of derivative securities in financial markets modeled by a sub-mixed fractional Brownian motion with jumps (smfBm-J), a non-Markovian process that captures both long-range dependence and jump discontinuities. Under this…
This paper deals with the notion of a large financial market and the concepts of asymptotic arbitrage and strong asymptotic arbitrage (both of the first kind), introduced by Yu.M. Kabanov and D.O. Kramkov. We show that the arbitrage…