scholarly journals Reduced-form setting under model uncertainty with non-linear affine intensities

2021 ◽  
Vol 6 (3) ◽  
pp. 159
Author(s):  
Francesca Biagini ◽  
Katharina Oberpriller
Keyword(s):  
Parameter Uncertainty ◽  
Model Uncertainty ◽  
Classical Case ◽  
Reduced Form ◽  
Contingent Claim ◽  
No Arbitrage ◽  
Affine Process ◽  
Non Linear

<p style='text-indent:20px;'>In this paper we extend the reduced-form setting under model uncertainty introduced in [<xref ref-type="bibr" rid="b5">5</xref>] to include intensities following an affine process under parameter uncertainty, as defined in [<xref ref-type="bibr" rid="b15">15</xref>]. This framework allows us to introduce a longevity bond under model uncertainty in a way consistent with the classical case under one prior and to compute its valuation numerically. Moreover, we price a contingent claim with the sublinear conditional operator such that the extended market is still arbitrage-free in the sense of “no arbitrage of the first kind” as in [<xref ref-type="bibr" rid="b6">6</xref>]. </p>

Nearly Exact Bayesian Estimation of Non-linear No-Arbitrage Term-Structure Models*

2021 ◽  
Author(s):  
Marcello Pericoli ◽  
Marco Taboga
Keyword(s):  
Bayesian Estimation ◽  
Term Structure ◽  
Broad Class ◽  
Model Parameters ◽  
State Variables ◽  
Computationally Efficient ◽  
Macroeconomic Factors ◽  
No Arbitrage ◽  
Term Structure Models ◽  
Non Linear

Abstract We propose a general method for the Bayesian estimation of a very broad class of non-linear no-arbitrage term-structure models. The main innovation we introduce is a computationally efficient method, based on deep learning techniques, for approximating no-arbitrage model-implied bond yields to any desired degree of accuracy. Once the pricing function is approximated, the posterior distribution of model parameters and unobservable state variables can be estimated by standard Markov Chain Monte Carlo methods. As an illustrative example, we apply the proposed techniques to the estimation of a shadow-rate model with a time-varying lower bound and unspanned macroeconomic factors.

Efficient dynamic analysis of a whole aeroengine using identified nonlinear bearing models

2011 ◽  
Vol 226 (1) ◽  
pp. 66-81 ◽  
Author(s):  
K H Groves ◽  
P Bonello ◽  
P M Hai
Keyword(s):  
Dynamic Performance ◽  
Computational Cost ◽  
Parametric Identification ◽  
Frequency Domain Analysis ◽  
Reduced Form ◽  
Squeeze Film ◽  
Computational Time ◽  
Parameter Study ◽  
Accurate Identification ◽  
Non Linear

Essential to effective aeroengine design is the rapid simulation of the dynamic performance of a variety of engine and non-linear squeeze-film damper (SFD) bearing configurations. Using recently introduced non-linear solvers combined with non-parametric identification of high-accuracy bearing models it is possible to run full-engine rotordynamic simulations, in both the time and frequency domains, at a fraction of the previous computational cost. Using a novel reduced form of Chebyshev polynomial fits, efficient and accurate identification of the numerical solution to the two-dimensional Reynolds equation (RE) is achieved. The engine analysed is a twin-spool five-SFD engine model provided by a leading manufacturer. Whole-engine simulations obtained using Chebyshev-identified bearing models of the finite difference (FD) solution to the RE are compared with those obtained from the original FD bearing models. For both time and frequency domain analysis, the Chebyshev-identified bearing models are shown to mimic accurately and consistently the simulations obtained from the FD models in under 10 per cent of the computational time. An illustrative parameter study is performed to demonstrate the unparalleled capabilities of the combination of recently developed and novel techniques utilised in this paper.

scholarly journals Mean-Variance Hedging Based on an Incomplete Market with External Risk Factors of Non-Gaussian OU Processes

2015 ◽  
Vol 2015 ◽  
pp. 1-20
Author(s):  
Wanyang Dai
Keyword(s):  
Risk Factors ◽  
Financial Market ◽  
Contingent Claim ◽  
Global Risk ◽  
Hedging Strategy ◽  
Put Options ◽  
No Arbitrage ◽  
Special Cases ◽  
External Risk ◽  
Non Gaussian

We prove the global risk optimality of the hedging strategy of contingent claim, which is explicitly (or called semiexplicitly) constructed for an incomplete financial market with external risk factors of non-Gaussian Ornstein-Uhlenbeck (NGOU) processes. Analytical and numerical examples are both presented to illustrate the effectiveness of our optimal strategy. Our study establishes the connection between our financial system and existing general semimartingale based discussions by justifying required conditions. More precisely, there are three steps involved. First, we firmly prove the no-arbitrage condition to be true for our financial market, which is used as an assumption in existing discussions. In doing so, we explicitly construct the square-integrable density process of the variance-optimal martingale measure (VOMM). Second, we derive a backward stochastic differential equation (BSDE) with jumps for the mean-value process of a given contingent claim. The unique existence of adapted strong solution to the BSDE is proved under suitable terminal conditions including both European call and put options as special cases. Third, by combining the solution of the BSDE and the VOMM, we reach the justification of the global risk optimality for our hedging strategy.

scholarly journals Computer-aided SPT-based reliability model for probability of liquefaction using hybrid PSO and GA

2020 ◽  
Vol 7 (1) ◽  
pp. 107-127 ◽  
Author(s):  
Maral Goharzay ◽  
Ali Noorzad ◽  
Ahmadreza Mahboubi Ardakani ◽  
Mostafa Jalal
Keyword(s):  
Engineering Design ◽  
Parameter Uncertainty ◽  
Model Uncertainty ◽  
Probabilistic Method ◽  
Limit State ◽  
Soil Liquefaction ◽  
Probability Models ◽  
Reliability Indices ◽  
Hybrid Particle Swarm Optimization ◽  
Reliability Method

Abstract In this paper, an approach for soil liquefaction evaluation using probabilistic method based on the world-wide SPT databases has been presented. In this respect, the parameters’ uncertainties for liquefaction probability have been taken into account. A calibrated mapping function is developed using Bayes’ theorem in order to capture the failure probabilities in the absence of the knowledge of parameter uncertainty. The probability models provide a simple, but also efficient decision-making tool in engineering design to quantitatively assess the liquefaction triggering thresholds. Within an extended framework of the first-order reliability method considering uncertainties, the reliability indices are determined through a well-performed meta-heuristic optimization algorithm called hybrid particle swarm optimization and genetic algorithm to find the most accurate liquefaction probabilities. Finally, the effects of the level of parameter uncertainty on liquefaction probability, as well as the quantification of the limit state model uncertainty in order to incorporate the correct model uncertainty, are investigated in the context of probabilistic reliability analysis. The results gained from the presented probabilistic model and the available models in the literature show the fact that the developed approach can be a robust tool for engineering design and analysis of liquefaction as a natural disaster.

Robust Optimization With Mixed Interval and Probabilistic Parameter Uncertainties, Model Uncertainty, and Metamodeling Uncertainty

2019 ◽  
Author(s):  
Yanjun Zhang ◽  
Tingting Xia ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Real World ◽  
Parameter Uncertainty ◽  
Model Uncertainty ◽  
Optimization Problems ◽  
Probability Distributions ◽  
Parameter Uncertainties ◽  
True Value ◽  
Uncertainty Model ◽  
The Difference

Abstract Various types of uncertainties, such as parameter uncertainty, model uncertainty, metamodeling uncertainty may lead to low robustness. Parameter uncertainty can be either epistemic or aleatory in physical systems, which have been widely represented by intervals and probability distributions respectively. Model uncertainty is formally defined as the difference between the true value of the real-world process and the code output of the simulation model at the same value of inputs. Additionally, metamodeling uncertainty is introduced due to the usage of metamodels. To reduce the effects of uncertainties, robust optimization (RO) algorithms have been developed to obtain solutions being not only optimal but also less sensitive to uncertainties. Based on how parameter uncertainty is modeled, there are two categories of RO approaches: interval-based and probability-based. In real-world engineering problems, both interval and probabilistic parameter uncertainties are likely to exist simultaneously in a single problem. However, few works have considered mixed interval and probabilistic parameter uncertainties together with other types of uncertainties. In this work, a general RO framework is proposed to deal with mixed interval and probabilistic parameter uncertainties, model uncertainty, and metamodeling uncertainty simultaneously in design optimization problems using the intervals-of-statistics approaches. The consideration of multiple types of uncertainties will improve the robustness of optimal designs and reduce the risk of inappropriate decision-making, low robustness and low reliability in engineering design. Two test examples are utilized to demonstrate the applicability and effectiveness of the proposed RO approach.

LONG RANGE DEPENDENCE, NO ARBITRAGE AND THE BLACK–SCHOLES FORMULA

2002 ◽  
Vol 02 (02) ◽  
pp. 265-280 ◽  
Author(s):  
M. ZÄHLE
Keyword(s):  
Wiener Process ◽  
Long Range ◽  
Continuous Process ◽  
Classical Case ◽  
Quadratic Variation ◽  
Long Range Dependence ◽  
Fair Price ◽  
No Arbitrage ◽  
Black Scholes ◽  
Stock Model

A bond and stock model is considered where the driving process is the sum of a Wiener process W and a continuous process Z with zero generalized quadratic variation. By means of forward integrals a hedge against Markov-type claims is constructed. If Z is independent of W under some natural assumptions on Z and the admissible portfolio processes the model is shown to be arbitrage free. The fair price of the above claims agrees with that in the classical case Z ≡ 0. In particular, the Black–Scholes formula remains valid for non-semimartingale models with long range dependence.

Robust Optimization With Parameter and Model Uncertainties Using Gaussian Processes With Limited Samples

2017 ◽  
Author(s):  
Yanjun Zhang ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Engineering Design ◽  
Gaussian Processes ◽  
Parameter Uncertainty ◽  
Model Uncertainty ◽  
Computational Cost ◽  
Random Errors ◽  
Model Uncertainties ◽  
Uncertainty Model ◽  
Gp Model

Uncertainty is inevitable in engineering design. The existence of uncertainty may change the optimality and/or the feasibility of the obtained optimal solutions. In simulation-based engineering design, uncertainty could have various types of sources, such as parameter uncertainty, model uncertainty, and other random errors. To deal with uncertainty, robust optimization (RO) algorithms are developed to find solutions which are not only optimal but also robust with respect to uncertainty. Parameter uncertainty has been taken care of by various RO approaches. While model uncertainty has been ignored in majority of existing RO algorithms with the hypothesis that the simulation model used could represent the real physical system perfectly. In the authors’ earlier work, a RO framework was proposed to consider both parameter and model uncertainties using the Bayesian approach with Gaussian processes (GP), where metamodeling uncertainty introduced by GP modeling is ignored by assuming the constructed GP model is accurate enough with sufficient training samples. However, infinite samples are impossible for real applications due to prohibitive time and/or computational cost. In this work, a new RO framework is proposed to deal with both parameter and model uncertainties using GP models but only with limited samples. The compound effect of parameter, model, and metamodeling uncertainties is derived with the form of the compound mean and variance to formulate the proposed RO approach. The proposed RO approach will reduce the risk for the obtained robust optimal designs considering parameter and model uncertainties becoming non-optimal and/or infeasible due to insufficiency of samples for GP modeling. Two test examples with different degrees of complexity are utilized to demonstrate the applicability and effectiveness of the proposed approach.

Uncertainty in Product Modelling within the Development Process

2015 ◽  
Vol 807 ◽  
pp. 89-98 ◽  
Author(s):  
Jan Würtenberger ◽  
Sebastian Gramlich ◽  
Tillmann Freund ◽  
Julian Lotz ◽  
Maximilian Zocholl ◽  
...  
Keyword(s):  
Parameter Uncertainty ◽  
Model Uncertainty ◽  
Development Process ◽  
Product Model ◽  
Modelling Uncertainty ◽  
Model Based ◽  
Product Models ◽  
Product Modelling ◽  
Uncertainty Parameter

This paper gives an overview about how to locate uncertainty in product modelling within the development process. Therefore, the process of product modelling is systematized with the help of characteristics of product models and typical working steps to develop a product model. Based on that, it is possible to distinguish between product modelling uncertainty, mathematic modelling uncertainty, parameter uncertainty, simulation uncertainty and product model uncertainty.

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