Some Large Deviations Results for Latin Hypercube Sampling

Large deviations theory is a well-studied area which has shown to have numerous applications. Broadly speaking, the theory deals with analytical approximations of probabilities of certain types of rare events. Moreover, the theory has recently proven instrumental in the study of complexity of methods that solve stochastic optimization problems by replacing expectations with sample averages (such an approach is called sample average approximation in the literature). The typical results, however, assume that the underlying random variables are either i.i.d. or exhibit some form of Markovian dependence. Our interest in this paper is to study the application of large deviations results in the context of estimators built with Latin Hypercube sampling, a well-known sampling technique for variance reduction. We show that a large deviation principle holds for Latin Hypercube sampling for functions in one dimension and for separable multi-dimensional functions. Moreover, the upper bound of the probability of a large deviation in these cases is no higher under Latin Hypercube sampling than it is under Monte Carlo sampling. We extend the latter property to functions that are monotone in each argument. Numerical experiments illustrate the theoretical results presented in the paper.     

Synthesis of Rhodomyrtone Analogs Modified at C7

We developed a route to rhodomyrtone analogs that feature different acyl groups at C7. Since electrophilic substitution reactions on the aryl part of the rhodomyrtone core led to C5 derivatives, the C5 position was blocked by a chlorine. Subsequent Duff type formylation followed by Grignard addition to the aldehyde group and oxidation gave various phenones. The benzyl protecting groups were removed by hydrogenation or boron tribromide. Some derivatives turned out to be quite active against multiple resistant Staphylococcus aureus strains and a rhodomyrtone resistant mutant (Rom^R). The chlorine at C5 seems to have a beneficial effect on the antibacterial activity.     

Time series model for GLWB with surrender benefit and stochastic interest rate: Dynamic withdrawal approach

This study investigates the pricing problem of a variable annuity (VA) contract embedded with a guaranteed lifetime withdrawal benefit (GLWB) rider. VAs are annuities in which the value is linked to a bond and equity sub-account fund. The guaranteed lifetime withdrawal benefit rider regularly provides a series of payments to the policyholder for the term of the policy while he/she is alive, regardless of portfolio performance. At the time of the policyholder's death, the remaining fund value is given to his nominee. Therefore, proper fund modeling is critical in the pricing of VA products. Several writers in the literature used a GBM model in which variance is considered to be constant to represent the fund value in a variable annuity contract. However, on the other hand, the returns on financial assets are non-normally distributed in real life. A bit much Kurtosis, leverage effect, and Non-zero Skewness characterize the returns. The generalized autoregressive conditional heteroscedastic (GARCH) models are also used for presenting a discrete framework for the pricing of GLWB. Still, the interest rate was kept constant without including the surrender benefit and the static withdrawal approach, which keeps the model far from the real scenario. Thus, in this research, the generalized GARCH models are used with surrender benefit and dynamic withdrawal strategy to develop a time series model for the pricing of annuity that overcomes the constraints of previous models. A numerical illustration and sensitivity analysis are used to examine the suggested model.