Importance Sampling for Credit Portfolio Risk with Risk Factors Having t-Copula

2017 ◽  
Vol 16 (04) ◽  
pp. 1101-1124 ◽  
Author(s):  
Rongda Chen ◽  
Ze Wang ◽  
Lean Yu
Keyword(s):  
Risk Factors ◽  
Importance Sampling ◽  
Variance Reduction ◽  
Heavy Tails ◽  
Risk Measure ◽  
Optimization Technique ◽  
Tail Probability ◽  
Portfolio Risk ◽  
Marquardt Algorithm ◽  
Credit Portfolio

This paper proposes an efficient simulation method for calculating credit portfolio risk when risk factors have a heavy-tailed distributions. In modeling heavy tails, its features of return on underlying asset are captured by multivariate [Formula: see text]-Copula. Moreover, we develop a three-step importance sampling (IS) procedure in the [Formula: see text]-copula credit portfolio risk measure model for further variance reduction. Simultaneously, we apply the Levenberg–Marquardt algorithm associated with nonlinear optimization technique to solve the problem that estimates the mean-shift vector of the systematic risk factors after the probability measure change. Numerical results show that those methods developed in the [Formula: see text]-copula model can produce large variance reduction relative to the plain Monte Carlo method, to estimate more accurately tail probability of credit portfolio loss distribution.

Analysis of credit portfolio risk using hierarchical multifactor models

2014 ◽  
Vol 10 (4) ◽  
pp. 45-70 ◽  
Author(s):  
Pak-Wing Fok ◽  
Xiuling Yan ◽  
Guangming Yao
Keyword(s):  
Portfolio Risk ◽  
Multifactor Models ◽  
Credit Portfolio

scholarly journals On the optimal importance process for piecewise deterministic Markov process

2019 ◽  
Vol 23 ◽  
pp. 893-921
Author(s):  
H. Chraibi ◽  
A. Dutfoy ◽  
T. Galtier ◽  
J. Garnier
Keyword(s):  
Importance Sampling ◽  
Simulation Study ◽  
Variance Reduction ◽  
Sampling Method ◽  
Piecewise Deterministic Markov Process ◽  
Importance Sampling Method ◽  
Markovian Processes ◽  
Component Systems ◽  
Reference Measure ◽  
Reduction Methods

In order to assess the reliability of a complex industrial system by simulation, and in reasonable time, variance reduction methods such as importance sampling can be used. We propose an adaptation of this method for a class of multi-component dynamical systems which are modeled by piecewise deterministic Markovian processes (PDMP). We show how to adapt the importance sampling method to PDMP, by introducing a reference measure on the trajectory space. This reference measure makes it possible to identify the admissible importance processes. Then we derive the characteristics of an optimal importance process, and present a convenient and explicit way to build an importance process based on theses characteristics. A simulation study compares our importance sampling method to the crude Monte-Carlo method on a three-component systems. The variance reduction obtained in the simulation study is quite spectacular.

Credit Portfolio Risk and Diversification

2013 ◽  
pp. 153-170
Author(s):  
Rudi Schäfer ◽  
Alexander F. R. Koivusalo ◽  
Thomas Guhr
Keyword(s):  
Portfolio Risk ◽  
Credit Portfolio

Modeling for Optimization (MO-OP): Tools for Manufacturing and Design Engineering Problems

2001 ◽  
Author(s):  
Mohamed H. Gadallah ◽  
Hazim El-Mounayri
Keyword(s):  
Variance Reduction ◽  
Optimization Technique ◽  
Tolerance Allocation ◽  
Process Selection ◽  
Engineering Problems ◽  
Simulation Results ◽  
Standard Designs ◽  
Performance Of Algorithm ◽  
Composite Designs

Abstract In this paper, a new statistical optimization technique is proposed. The technique employs new variance reduction schemes (VRTs). The performance of three standard designs: L27/L27 OA, L54/L27 OA and L243 / L27 OA are studied. These designs, although both orthogonal and balanced, exhibit high variance reduction properties with questionable convergence in very short number of iterations. Four new composite designs are developed, implemented and compared with the standard ones. These designs are known as: 5-, 7-, 9- and 11-point composite L27 OA. The problem of tolerance allocation with optimal process selection is revisited as a case study for simulation. Results indicate the efficiency of these new designs to reduce variances to lower levels than standard designs and better convergence in fraction of experiments. These designs are then integrated in an optimization algorithm previously developed (Gadallah, M.H., 2000). The algorithm is then modified to deal with the least sensitive optimal solutions for standard and composite designs. Particularly, the parameters that affect the algorithm are varied and their effects on performance of algorithm are studied. A standard manufacturing case study is used for analysis and simulation results for the composite designs are also given.

scholarly journals Optimal heavy tail estimation – Part 1: Order selection

2017 ◽  
Vol 24 (4) ◽  
pp. 737-744 ◽  
Author(s):  
Manfred Mudelsee ◽  
Miguel A. Bermejo
Keyword(s):  
Time Series ◽  
Heavy Tails ◽  
Characteristic Exponent ◽  
Tail Probability ◽  
Heavy Tail ◽  
Infinite Variance ◽  
Accurate Estimation ◽  
Monte Carlo Experiment ◽  
River Elbe ◽  
Tail Estimation

Abstract. The tail probability, P, of the distribution of a variable is important for risk analysis of extremes. Many variables in complex geophysical systems show heavy tails, where P decreases with the value, x, of a variable as a power law with a characteristic exponent, α. Accurate estimation of α on the basis of data is currently hindered by the problem of the selection of the order, that is, the number of largest x values to utilize for the estimation. This paper presents a new, widely applicable, data-adaptive order selector, which is based on computer simulations and brute force search. It is the first in a set of papers on optimal heavy tail estimation. The new selector outperforms competitors in a Monte Carlo experiment, where simulated data are generated from stable distributions and AR(1) serial dependence. We calculate error bars for the estimated α by means of simulations. We illustrate the method on an artificial time series. We apply it to an observed, hydrological time series from the River Elbe and find an estimated characteristic exponent of 1.48 ± 0.13. This result indicates finite mean but infinite variance of the statistical distribution of river runoff.

scholarly journals Design of Robust Fuzzy Logic Controller Based on the Levenberg Marquardt Algorithm and Fault Ride Trough Strategies for a Grid-Connected PV System

Electronics ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 429 ◽  
Author(s):  
Islam ◽  
Zeb ◽  
Din ◽  
Khan ◽  
Ishfaq ◽  
...  
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Logic Controller ◽  
Fault Tolerant ◽  
Optimization Technique ◽  
Line Length ◽  
Photovoltaic System ◽  
Pv System ◽  
Simulink Model ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt

This paper emphasizes the design and investigation of a new optimization scheme for a grid-connected photovoltaic system (PVS) under unbalance faults. The proposed scheme includes fuzzy logic controller (FLC) based on the Levenberg–Marquardt (LM) optimization technique in coordination with bridge-type-fault-current limiter (BFCL) as the fault ride through (FRT) Strategy. The LM optimization-based control is an iterative process with a fast and robust response and is always convergent. The BFCL reduces the fault currents to rated values without compromising at ripples. A keen and critical comparison of the designed strategy is carried out with a conventionally tuned proportional-integral (PI) controller in coordination with the crowbar FRT strategy. A 100kW MATLAB/Simulink model of a photovoltaic system is used for simulation and analysis of unbalance faults at the point of common-coupling (PCC) and at 5 km away from PCC. It is found that grid-connected PVS is highly influenced by the fault type and less effected by the distribution line length. The simulation results authenticated smooth, stable, ripples with free, robust, and fault-tolerant behavior of the proposed scheme.

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