arXiv subjects

Jean-Philippe Chancelier

Publications and source records attributed to Jean-Philippe Chancelier.

59 records · Page 4Linked to original sources

arXiv2012

Using Premia and Nsp for Constructing a Risk Management Benchmark for Testing Parallel Architecture

Financial institutions have massive computations to carry out overnight which are very demanding in terms of the consumed CPU. The challenge is to price many different products on a cluster-like architecture. We have used the Premia software to valuate the financial derivatives. In this work, we explain how Premia can be embedded into Nsp, a scientific software like Matlab, to provide a powerful tool to valuate a whole portfolio. Finally, we have integrated an MPI toolbox into Nsp to enable to use Premia to solve a bunch of pricing problems on a cluster. This unified framework can then be used to test different parallel architectures.

cs.CE↗

arXiv2010

Dynamic consistency for Stochastic Optimal Control problems

For a sequence of dynamic optimization problems, we aim at discussing a notion of consistency over time. This notion can be informally introduced as follows. At the very first time step $t_0$, the decision maker formulates an optimization problem that yields optimal decision rules for all the forthcoming time step $t_0, t_1, ..., T$; at the next time step $t_1$, he is able to formulate a new optimization problem starting at time $t_1$ that yields a new sequence of optimal decision rules. This process can be continued until final time $T$ is reached. A family of optimization problems formulated in this way is said to be time consistent if the optimal strategies obtained when solving the original problem remain optimal for all subsequent problems. The notion of time consistency, well-known in the field of Economics, has been recently introduced in the context of risk measures, notably by Artzner et al. (2007) and studied in the Stochastic Programming framework by Shapiro (2009) and for Markov Decision Processes (MDP) by Ruszczynski (2009). We here link this notion with the concept of "state variable" in MDP, and show that a significant class of dynamic optimization problems are dynamically consistent, provided that an adequate state variable is chosen.

math.OC↗

arXiv2009

A note on strong convergence to common fixed points of nonexpansive mappings in Hilbert spaces

The aim of this paper is to investigate the links between ${\cal T}_C$-class algorithms, CQ Algorithm and shrinking projection methods. We show that strong convergence of these algorithms are related to coherent ${\cal T}_C$-class sequences of mapping. Some examples dealing with nonexpansive finite set of mappings and nonexpansive semigroups are given. They extend some existing theorems.

math.OC↗

arXiv2007

Iterative schemes for computing fixed points of nonexpansive mappings in Banach spaces

Let $X$ be a real Banach space with a normalized duality mapping uniformly norm-to-weak$^\star$ continuous on bounded sets or a reflexive Banach space which admits a weakly continuous duality mapping $J_Φ$ with gauge $ϕ$. Let $f$ be an {\em $α$-contraction} and $\{T_n\}$ a sequence of nonexpansive mapping, we study the strong convergence of explicit iterative schemes x_{n+1} = α_n f(x_n) + (1-α_n) T_n x_n with a general theorem and then recover and improve some specific cases studied in the literature

math.OC↗

arXiv2007

${\cal T}$-class algorithms for pseudocontractions and $κ$-strict pseudocontractions in Hilbert spaces

In this paper we study iterative algorithms for finding a common element of the set of fixed points of $κ$-strict pseudocontractions or finding a solution of a variational inequality problem for a monotone, Lipschitz continuous mapping. The last problem being related to finding fixed points of pseudocontractions. These algorithms were already studied in [G.L. Acedo, H.-K. Xu] and [N. Nadezhkina, W. Takahashi] but our aim here is to provide the links between these know algorithms and the general framework of ${\cal T}$-class algorithms studied in [H.H. Bauschke, P.L. Combettes].

math.OC↗