Narrow Results

Reliability of a software application, its failure intensity and the residual number of faults are three important metrics that provide a quantitative assessment of the failure characteristics of an application. Ultimately, it is also necessary, based on these metrics, to determine an optimal release time at which costs justify the stop test decision. Typically, one of the many stochastic models known as software reliability growth models (SRGMs) is used to characterize the failure behavior of an application to provide estimates of the failure intensity, residual number of faults, reliability, and optimal release time and cost. To ensure analytical tractability, SRGMs assume instantaneous repair and thus the estimates of these metrics obtained using SRGMs tend to be optimistic. In practice, repair activity consumes a non trivial amount of time and resources. Also, repair may be conducted according to many policies which reflect the schedule and budget constraints of a project. A few efforts which incorporate repair into SRGMs are restrictive, since they consider only some SRGMs, model the repair process using a constant repair rate, and provide an estimate of only the residual number of faults. These efforts do not address the issue of estimating the failure intensity, reliability and optimal release time and cost in the presence of repair. In this paper we present a generic framework based on the rate-based simulation technique to incorporate repair policies into finite failure non homogeneous Poisson process (NHPP) class of SRGMs. We describe a methodology to compute the failure intensity and reliability in the presence of repair, and apply it to four popular finite failure NHPP models. We also present an economic cost model which considers explicit repair in providing estimates of optimal release time and cost. We illustrate the potential of the framework to quantify the impact of the parameters of the repair policies on the above metrics using examples. Through these examples we discuss how the framework could be used to guide the allocation of resources to achieve the desired reliability target in a cost-effective manner.

The early exercise premium and the price of an American put option are evaluated by using nonparametric regression on the time to expiration, the moneyness and the volatility of underlying assets. In terms of mean square error (MSE), our nonparametric methods of American put option pricings outperform the existing classical methods for both in-the-sample (1 September 2011–31 January 2012) and out-of-sample (1 September 2012–28 February 2013) testings on the S&P 100 Index (OEX). Our methods have better predictions and more accurate approximations. The Greek letters for both the early exercise premium and the American put option are computed numerically.

In this paper, we study the optimal stopping time and the optimal stopping boundary for the perpetual Russian option under the diffusion process. The general continuation region is characterized by a function b(p,t) depending on both variables t and the maximum value of the stock and initial starting value P₀. Previous studies assume that the continuation region is given by a function depending upon the time t only. This is unreal hypothesis for the diffusion to achieve. Our result shows that the perpetual Russian option can be described by a Black–Scholes equation over the continuation region and smooth boundary conditions on the optimal stopping boundary. Furthermore, we develop an evaluation method from the lookback option on a stopping time, and establish the Greek letters for the perpetual Russian option. We obtain the exact upper bound for the prices of the perpetual Russian options and demonstrate that both the payoff and the optimal stopping time are path-dependent by Monte Carlo simulations.

American options are important financial products traded in enormous volumes across the world. Therefore, accurate and efficient valuation is of paramount importance for global financial markets. Due to the early exercise feature, the pricing of American options is significantly more complicated than European options, and an analytical closed-form solution is unavailable even for simple dynamic models. Practitioners employ various valuation methods to strike the balance: accurate valuation usually suffers inefficiency, while fast valuation likely leads to inaccuracy. In this paper, we provide an innovative solution to address both the accuracy and efficiency issues of pricing American options by applying quantum reinforcement learning. Meanwhile, the quantum part of the new approach would potentially speed up the calculation dramatically.