No abstract

The coherent risk framework has been introduced by Artzner et al. (1999) Concerning the problem of computing hedges that optimize the degree of acceptability of a given position, we provide sufficient conditions under which an algorithm of dynamic programming type can be applied. For the special case of a derivative on a single underlying with convex payoff, and for a particular class of acceptability measures, we show that this algorithm simplifies considerably and we give explicit formulas for hedges that maximize the degree of acceptability.

No abstract

General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research-You may not further distribute the material or use it for any profit-making activity or commercial gain-You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim.

In this paper we consider open-loop Nash equilibria of the linear-quadratic differential game. We present both necessary and sufficient conditions for existence of a unique solution for the finite-planning horizon case, and show that there exist situations where the set of associated Riccati differential equations has no solution, whereas the problem does have an equilibrium. The pursued analyses allows a simple study of convergence of the equilibrium strategy if the planning horizon expands. Conditions are given under which this strategy converges. A detailed study of the infinite planning horizon case is given. In particular we show that, in general, this problem has not a unique equilibrium. Furthermore, we show that the limit of the above mentioned converged strategy may be not an equilibrium for the infinite planning horizon problem. Particular attention is paid to computational aspects and the scalar case.