Learn More
This paper concerns the optimal stopping time problem in a nite horizon of a controlled jump diiusion process. We prove that the value function is continuous and is a viscosity solution of the inte-grodiierential variational inequality arising from the associated dynamic programming. We also establish comparison principles, which yield uniqueness results.(More)
We review the main results in the theory of quadratic hedging in a general incomplete model of continuous trading with semimartingale price process. The objective is to hedge contingent claims by using portfolio strategies. We describe two types of criteria: the so-called (local) risk-minimization and the mean-variance approaches. From a mathematical(More)
We study a financial market with incompleteness arising from two sources: stochastic volatility and portfolio constraints. The latter are given in terms of bounds imposed on the borrowing and short-selling of a ‘hedger’ in this market, and can be described by a closed convex set K . We find explicit characterizations of the minimal price needed to(More)
We study the problem of nding the minimal price needed to dominate European-type contingent claims under proportional transaction costs in a continuous-time diiu-sion model. The result we prove has already been known in special cases-the minimal super-replicating strategy is the least expensive buy-and-hold strategy. Our contribution consists in showing(More)
Let X be a special semimartingale of the form X = X0 + M + ∫ d〈M〉 λ̂, denote by K̂ = ∫ λ̂ d〈M〉 λ̂ the mean-variance tradeoff process of X and by Θ the space of predictable processes θ for which the stochastic integral G(θ) = ∫ θdX is a square-integrable semimartingale. For a given constant c ∈ IR and a given square-integrable random variable H, the(More)