Optimization strategies in credit portfolio management

Abstract

-This paper focuses on the application of an original global optimization algorithm, based on the hybridization between a genetic algorithm and a semi-deterministic algorithm, for the resolution of various constrained optimization problems for realistic credit portfolios. Results are analyzed from a financial point of view in order to confirm their relevance.

A Variance-Expected Compliance Model for Structural Optimization

“…More precisely, to study the robustness of each structure λ (α,β) , we consider the random variable Ψ (α,β) = Ψ(ξ, λ (α,β) ) and we approximate its density function ρ Ψ (α,β) using a Monte-Carlo approach [19] (i.e. generating M ∈ IN values of ξ).…”

“…Risk measures on L ∞ (Ω, A, IP) are mapping ̟ : L ∞ (Ω, A, IP) → IR where (Ω, A, IP) is a probability space (a complete presentation can be found in [6]). They are used in various areas, such as financial analysis [19], in order to study the value of the worst case scenarios (in our case, the random loads which generate the highest compliances of the structure). Here we focus on a particular and popular risk measure called the Coherent-Value at Risk (C-VaR) [5], defined as: .25)).…”

An expected compliance model based on topology optimization for designing structures submitted to random loads

“…In general cases, it could be difficult to evaluate directly IE[Ψ(ξ , ρ)]. We can consider, for instance, a Monte-Carlo algorithm (see [10]) to approximate those values. However, this method, and thus the resolution of (8), is numerically expensive.…”

“…The gradient of the functional to be minimized is approximated with a first order finite difference approach. A complete description and validation of this algorithm can be found in [10,11]. The obtained solutions are denoted by ρ sp for Problem (6)- (7) and ρ ec for Problem (10)- (13) .…”

“…Then, for each solution ρ ∈ {ρ sp , ρ ec } , we consider the random variable Φ ρ = Ψ(ξ , ρ). We approximate the density function of Φ ρ , denoted by γ Φ ρ , by using a Monte-Carlo approach [10] that generates M ∈ IN possible scenarios (i.e., values of ξ ). Then, we calculate some statistical values of γ Φ ρ : its mean, maximum and 1%-Coherent-Value at Risk (C-VaR 1 ) values.…”