Related papers: Efficient hedging under ambiguity in continuous ti…
In this paper we derive robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating…
We consider the pricing problem facing a seller of a contingent claim. We assume that this seller has some general level of partial information, and that he is not allowed to sell short in certain assets. This pricing problem, which is our…
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…
In a model free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a…
We study contingent claims in a discrete-time market model where trading costs are given by convex functions and portfolios are constrained by convex sets. In addition to classical frictionless markets and markets with transaction costs or…
The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in…
In a discrete-time financial market, a generalized duality is established for model-free superhedging, given marginal distributions of the underlying asset. Contrary to prior studies, we do not require contingent claims to be upper…
Explicit robust hedging strategies for convex or concave payoffs under a continuous semimartingale model with uncertainty and small transaction costs are constructed. In an asymptotic sense, the upper and lower bounds of the cumulative…
We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitrage-free prices.…
We consider as given a discrete time financial market with a risky asset and options written on that asset and determine both the sub- and super-hedging prices of an American option in the model independent framework of ArXiv:1305.6008. We…
This paper studies convex duality in optimal investment and contingent claim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions…
We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of…
The classical discrete time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing for convex transaction…
We study the superreplication of contingent claims under model uncertainty in discrete time. We show that optimal superreplicating strategies exist in a general measure-theoretic setting; moreover, we characterize the minimal…
We consider the pricing problem of a seller with delayed price information. By using Lagrange duality, a dual problem is derived, and it is proved that there is no duality gap. This gives a characterization of the seller's price of a…
Convex duality for two two different super--replication problems in a continuous time financial market with proportional transaction cost is proved. In this market, static hedging in a finite number of options, in addition to usual dynamic…
We present here a regress later based Monte Carlo approach that uses neural networks for pricing high-dimensional contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for…
The determination of acceptability prices of contingent claims requires the choice of a stochastic model for the underlying asset price dynamics. Given this model, optimal bid and ask prices can be found by stochastic optimization. However,…
We consider the problem of hedging a European contingent claim in a Bachelier model with transient price impact as proposed by Almgren and Chriss. Following the approach of Rogers and Singh and Naujokat and Westray, the hedging problem can…
We provide a model-free pricing-hedging duality in continuous time. For a frictionless market consisting of $d$ risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging…