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The front bearing mount structure in an aero engine has been severely loaded under the fan blade off (FBO) event since imbalance forces at high amplitude but low frequency is transformed to the engine front mount structure. The bearing mount structural forces are estimated by an integrated implicit-explicit analysis process of whole engine model of an aero engine. Since there are many dependent factors which are governing those predicted loads, experimental evidence on FBO is becoming necessary to validate the model used for the load prediction which is more expensive and also time consuming. This paper aims to discuss the above mentioned issues.

The current paper deals with the high impact but low probability nature of FBO load prediction on the bearing mount structure by stochastic approach which could be replaced for FBO experiments which is highly essential for current economic conditions. Several influential factors on the predicted loads have been chosen in the stochastic model and sensitive analysis has also been performed to bring down the variation involved in the predicted load.

The predicted load by proposed stochastic model is then compared with the experimental results. The conclusion on the predicted load with various dependent influential factors is matching well with certain value of damage factor from planned FBO test event.

Limitation of this paper could be that it does not cover with range of load amplitude and is only applicable for civil small and medium engines.

The high amplitude but low frequency load pattern is assessed with impact condition by stochastic model.

Combining experimental and probabilistic load prediction was never done before and read across from previous engine test program could be effectively performed with stochastic model approach.

How do stock prices evolve over time? The standard assumption of geometric Brownian motion, questionable as it has been right along, is even more doubtful in light of the recent stock market crash and the subsequent prices of U.S. index options. With the development of rich and deep markets in these options, it is now possible to use options prices to make inferences about the risk-neutral stochastic process governing the underlying index. We compare the ability of models including Black–Scholes, naïve volatility smile predictions of traders, constant elasticity of variance, displaced diffusion, jump diffusion, stochastic volatility, and implied binomial trees to explain otherwise identical observed option prices that differ by strike prices, times-to-expiration, or times. The latter amounts to examining predictions of future implied volatilities.

Certain naïve predictive models used by traders seem to perform best, although some academic models are not far behind. We find that the better-performing models all incorporate the negative correlation between index level and volatility. Further improvements to the models seem to require predicting the future at-the-money implied volatility. However, an “efficient markets result” makes these forecasts difficult, and improvements to the option-pricing models might then be limited.

The purpose of this paper is to investigate the first three stochastic natural frequencies of skewed sandwich plates, considering uncertain system parameters. To conduct the sensitivity analysis for checking the criticality of input parameters.

The theoretical formulation is developed based on higher-order-zigzag theory in accordance with the radial basis function (RBF) and stochastic finite element (FE) model. A cubic function is considered for in-plane displacement over thickness while a quadratic function is considered for transverse displacement within the core and remains constant in the facesheet. RBF is used as a surrogate model to achieve computational efficiency and accuracy. In the present study, the individual and combined effect of ply-orientation angle, skew angle, number of lamina, core thickness and material properties are considered for natural frequency analysis of sandwich plates.

Results presented in this paper illustrates that the skewness in the sandwich plate significantly affects the global dynamic behaviour of the structure. RBF surrogate model coupled with stochastic FE approach significantly reduced the computational time (more than 1/18 times) compared to direct Monte Carlo simulation approach.

The stochastic results for dynamic stability of sandwich plates show that the inevitable source uncertainties present in the input parameters result in significant variation from the deterministic value demonstrates the need for inclusive design paradigm considering stochastic effects. The present paper comprehensively establishes a generalized new RBF-based FE approach for efficient stochastic analysis, which can be applicable to other complex structures too.

This chapter has been seminal work of Dr K.S.S. Iyer, which has taken time to develop, for over the last 56 years to be presented here. The method in advance predictive analytics has developed, from his several other applications, in predictive modeling by using the stochastic point process technique. In the chapter on advance predictive analytics, Dr Iyer is collecting his approaches and generalizing it in this chapter. In this chapter, two of the techniques of stochastic point process known as Product Density and Random point process used in modelling problems in High energy particles and cancer, are redefined to suit problems currently in demand in IoT and customer equity in marketing (Iyer, Patil, & Chetlapalli, 2014b). This formulation arises from these techniques being used in different fields like energy requirement in Internet of Things (IoT) devices, growth of cancer cells, cosmic rays’ study, to customer equity and many more approaches.

This chapter examines the effect of the division of labor from a Bayesian viewpoint. While organizational reforms are crucial for cost reduction in the Japanese water supply industry, the effect of labor division in intra-organizational units on total costs has, to the best of our knowledge, not been examined empirically. Fortunately, a one-time survey of 79 Japanese water suppliers conducted in 2010 enables us to examine the effect. To examine this problem, a cost stochastic frontier model with endogenous regressors is considered in a cross-sectional setting, because the cost and the division of labor are regarded as simultaneously determined factors. From the empirical analysis, we obtain the following results: (1) total costs rise when the level of labor division becomes high; (2) ignoring the endogeneity leads to the underestimation of the impact of labor division on total costs; and (3) the estimation bias on inefficiency can be mitigated for relatively efficient organizations by including the labor division variable in the model, while the bias for relatively inefficient organizations needs to be controlled by considering its endogeneity. In summary, our results indicate that integration of internal sections is better than specialization in terms of costs for Japanese water supply organizations.

The traditional predictor of technical inefficiency proposed by Jondrow, Lovell, Materov, and Schmidt (1982) is a conditional expectation. This chapter explores whether, and by how much, the predictor can be improved by using auxiliary information in the conditioning set. It considers two types of stochastic frontier models. The first type is a panel data model where composed errors from past and future time periods contain information about contemporaneous technical inefficiency. The second type is when the stochastic frontier model is augmented by input ratio equations in which allocative inefficiency is correlated with technical inefficiency. Compared to the standard kernel-smoothing estimator, a newer estimator based on a local linear random forest helps mitigate the curse of dimensionality when the conditioning set is large. Besides numerous simulations, there is an illustrative empirical example.

Longevity risk, that is, the uncertainty of the demographic survival rate, is an important risk for insurance companies and pension funds, which have large, and long‐term, exposures to survivorship. The purpose of this paper is to propose a new model to describe this demographic survival risk.

The model proposed in this paper satisfies all the desired properties of a survival rate and has an explicit distribution for both single years and accumulative years.

The results show that it is important to consider the expected shift and risk premium of life table uncertainty and the stochastic behaviour of survival rates when pricing the survivor derivatives.

This model can be applied to the rapidly growing market for survivor derivatives.

This paper studies the performance of commonly employed stochastic volatility and jump models in the consistent pricing of The CBOE Volatility Index (VIX) and The S&P 500 Index (SPX) options. With the existence of active markets for volatility derivatives and options on the underlying instrument, the need for models that are able to price these markets consistently has increased. Although pricing formulas for VIX and vanilla options are now available for commonly used models exhibiting stochastic volatility and/or jumps, it remains to be shown whether these are able to price both markets consistently. This paper fills this vacuum.

In particular, the Heston model, the Heston model with jumps in returns and the Heston model with simultaneous jumps in returns and variance (SVJJ) are jointly calibrated to market quotes on SPX and VIX options together with VIX futures.

The full flexibility of having jumps in both returns and volatility added to a stochastic volatility model is essential. Moreover, we find that the SVJJ model with the Feller condition imposed and calibrated jointly to SPX and VIX options fits both markets poorly. Relaxing the Feller condition in the calibration improves the performance considerably. Still, the fit is not satisfactory, and we conclude that one needs more flexibility in the model to jointly fit both option markets.

Compared to existing literature, we derive numerically simpler VIX option and futures pricing formulas in the case of the SVJ model. Moreover, the paper is the first to study the pricing performance of three widely used models to SPX options and VIX derivatives.

The purpose of this paper is to derive semi‐closed‐form solutions to a wide variety of interest rate derivatives prices under stochastic volatility in affine‐term structure models.

The paper first derives the Frobenius series solution to the cross‐moment generating function, and then inverts the related characteristic function using the Gauss‐Laguerre quadrature rule for the corresponding cumulative probabilities.

This paper values options on discount bonds, coupon bond options, swaptions, interest rate caps, floors, and collars, etc. The valuation approach suggested in this paper is found to be both accurate and fast and the approach compares favorably with some alternative methods in the literature.

Future research could extend the approach adopted in this paper to some non‐affine‐term structure models such as quadratic models.

The valuation approach in this study can be used to price mortgage‐backed securities, asset‐backed securities and credit default swaps. The approach can also be used to value derivatives on other assets such as commodities. Finally, the approach in this paper is useful for the risk management of fixed‐income portfolios.

This paper utilizes a new approach to value many of the most commonly traded interest rate derivatives in a stochastic volatility framework.