Sequential Design for Optimal Stopping Problems

We propose a new approach to solve optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff-Schwartz that focuses on approximating the stopping strategy. Namely, we introduce adaptive generation of the stochastic grids anchoring the simulated sample paths of the underlying state process. This allows for active learning of the classifiers partitioning the state space into the continuation and stopping regions. To this end, we examine sequential design schemes that adaptively place new design points close to the stopping boundaries. We then discuss dynamic regression algorithms that can implement such recursive estimation and local refinement of the classifiers. The new algorithm is illustrated with a variety of numerical experiments, showing that an order of magnitude savings in terms of design size can be achieved. We also compare with existing benchmarks in the context of pricing multi-dimensional Bermudan options.Comment: 24 page

The Determinants of Credit Ratings in the United Kingdom Insurance Industry

Executive Summary The Determinants of Credit Ratings in the United Kingdom Insurance Industry Academic researchers have devoted a considerable amount of attention to the activities of credit rating agencies over the past 20 years, focusing in particular on the agencies’ potential role in overseeing corporate financial strength and promoting the efficient operation of financial markets. Examinations of credit rating practices has recently extended to the insurance industry, where the complex technical nature of market transactions leads to policyholders, investors and others facing particularly acute information asymmetries at the point-of-sale. Published credit ratings are therefore seen as helping to alleviate imperfections in insurance markets by providing a third party opinion on the adequacy of an insurer’s financial health and the likelihood of it meeting obligations to policyholders and others in the future. Although the United Kingdom (UK) insurance market is now one of the five largest in the world, relatively little is known about the practices of the major firms and policy-makers which influence its operations. In particular, whilst the determinants of rating agencies’ assessments of United States (US) insurers is well documented, published studies have yet to provide comprehensive evidence about insurance company ratings in the UK. This study attempts to fill this gap by examining the ratings awarded by two of the world’s leading agencies – A.M. Best and Standard and Poor (S&P) – and establishing the extent to which organizational variables can help predict: (i) insurance firms’ decision to be rated; and (ii) the assigned ratings themselves. Our sample of UK data comprises ratings made by A.M. Best and S&P over the period 1993-1997 for both life and property-liability insurers. The panel data we use is ordinal in nature and is therefore analysed using an ordered probit model. However, because neither A.M. Best or S&P rate the full population of UK insurance firms our data set is potentially subject to selfselection bias and we therefore extend the model to correct for such problems. In particular, the paper examines the effect of eight firm-specific variables (namely, capital adequacy, profitability, liquidity, growth, size, mutual/stockowner status, reinsurance level, and short/long-term nature of business) on the ratings awarded by the two agencies, as well as on insurance firms’ decisions to volunteer for the ratings in the first place. In general terms, our evidence concurs with earlier US findings, and suggests that although the decision to be rated by either of the agencies is largely influenced by a common set of factors, the determinants of the ratings themselves appear to differ. Specifically, our first main finding is that insurers’ decisions to be rated by either A.M. Best or S&P is positively related to surplus growth, profitability and leverage. Second, while we find that A.M. Best’s ratings are positively linked to profitability and liquidity, as well as being generally higher for mutual insurers, the findings for S&P differ substantially. Although liquidity again exerted a positive influence on assigned ratings, the only other statistically significant variable was financial leverage, which had a negative sign. We believe that the results of our research are of potential importance for companies operating in insurance markets as well as for policy-makers, brokers and others. For example, the evidence that mutual insurers are generally assigned higher ratings than stock insurers suggests that certain publicly-traded insurers, in particular new entrants, might not possess sound financial strength and may require closer regulatory scrutiny than other, more established, insurance firms. In addition, the finding that liquidity has a significantly positive effect on ratings assigned by two of the world’s leading credit agencies should provide a measure of confidence about the robustness of the ratings to industry regulators, policyholders and investors in the UK. This could imply that external ratings might eventually play a role in substituting for costly industry regulation. The study concludes that although the factors influencing the decision to be rated by A.M. Best or S&P are broadly the same, a degree of variability exists in the variables which influence the actual ratings themselves. Insurance company managers should be aware of this when contemplating whether to seek an independent rating and which agency to choose for the assessment. We therefore believe that this study fills an important gap in the literature about key players in the important UK insurance market and provides a basis for the conduct of future research

The JPL Phase B interferometer testbed

Future NASA missions with large optical systems will require alignment stability at the nanometer level. However, design studies indicate that vibration resulting from on-board disturbances can cause jitter at levels three to four orders of magnitude greater than this. Feasibility studies have shown that a combination of three distinct control layers will be required for these missions, including disturbance isolation, active and passive structural vibration suppression, and active optical pathlength compensation. The CSI technology challenge is to develop these design and control approaches that can reduce vibrations in the optical train by a factor of 1000 to 10,000. The focus of the paper is on describing the Phase B Testbed structure and facility, as the experimental results are included in other papers presented at this same conference

Spatiotemporal evolution of radio wave pump-induced ionospheric phenomena near the fourth electron gyroharmonic

On 12 November 2001, the European Incoherent Scatter (EISCAT) high-frequency (HF) radio wave transmitter facility, operating in O-mode at 5.423 MHz with 550 MW effective radiated power, produced artificial optical rings which appeared immediately at transmitter turn-on and collapsed into blobs after ∼60 s while descending in altitude. A similar descent in altitude was observed in the EISCAT ultra high frequency (UHF) ion line enhancements. Likewise, the stimulated electromagnetic emission (SEE) spectra changed as the pump frequency approached the fourth electron gyroharmonic due to pump-induced variations in electron concentration. Optical recordings were made from Skibotn at 630.0 and 557.7 nm and from Ramfjord in white light. The altitude of the initial optical ring and steady state blob has been estimated by triangulation. The evolution in altitude of the optical emissions, ion line enhancements, and SEE spectra all show a similar morphology but are generally not at exactly the same height. Typically, the optical height is close to and a few kilometers below that of the radar backscatter but sometimes above it, both of which are above the SEE generation altitude. There is evidence that upper hybrid (UH) waves, which propagate perpendicular to the magnetic field line, and Langmuir (L) waves, which propagate parallel to the magnetic field line, act simultaneously to accelerate electrons even in the steady state

Replication or exploration? Sequential design for stochastic simulation experiments

We investigate the merits of replication, and provide methods for optimal design (including replicates), with the goal of obtaining globally accurate emulation of noisy computer simulation experiments. We first show that replication can be beneficial from both design and computational perspectives, in the context of Gaussian process surrogate modeling. We then develop a lookahead based sequential design scheme that can determine if a new run should be at an existing input location (i.e., replicate) or at a new one (explore). When paired with a newly developed heteroskedastic Gaussian process model, our dynamic design scheme facilitates learning of signal and noise relationships which can vary throughout the input space. We show that it does so efficiently, on both computational and statistical grounds. In addition to illustrative synthetic examples, we demonstrate performance on two challenging real-data simulation experiments, from inventory management and epidemiology.Comment: 34 pages, 9 figure

A New Galaxy in the Local Group: the Antlia Dwarf Galaxy

We report the discovery of new member of the Local Group in the constellation of Antlia. Optically the system appears to be a typical dwarf spheroidal galaxy of type dE3.5 with no apparent young blue stars or unusual features. A color-magnitude diagram in I, V-I shows the tip of the red giant branch, giving a distance modulus of 25.3 +/- 0.2 (1.15 Mpc +/- 0.1) and a metallicity of -1.6 +/- 0.3. Although Antlia is in a relatively isolated part of the Local Group it is only 1.2 degrees away on the sky from the Local Group dwarf NGC3109, and may be an associated system.Comment: AJ in press, 15 pages, 7 figures, figure 2 in b/w for space saving, full postscript version available at http://www.ast.cam.ac.uk/~gkth/antlia-pp.htm

Nonparametric Regression using the Concept of Minimum Energy

It has recently been shown that an unbinned distance-based statistic, the energy, can be used to construct an extremely powerful nonparametric multivariate two sample goodness-of-fit test. An extension to this method that makes it possible to perform nonparametric regression using multiple multivariate data sets is presented in this paper. The technique, which is based on the concept of minimizing the energy of the system, permits determination of parameters of interest without the need for parametric expressions of the parent distributions of the data sets. The application and performance of this new method is discussed in the context of some simple example analyses.Comment: 10 pages, 4 figure

Calculation of disease dynamics in a population of households

Early mathematical representations of infectious disease dynamics assumed a single, large, homogeneously mixing population. Over the past decade there has been growing interest in models consisting of multiple smaller subpopulations (households, workplaces, schools, communities), with the natural assumption of strong homogeneous mixing within each subpopulation, and weaker transmission between subpopulations. Here we consider a model of SIRS (susceptible-infectious-recovered-suscep​tible) infection dynamics in a very large (assumed infinite) population of households, with the simplifying assumption that each household is of the same size (although all methods may be extended to a population with a heterogeneous distribution of household sizes). For this households model we present efficient methods for studying several quantities of epidemiological interest: (i) the threshold for invasion; (ii) the early growth rate; (iii) the household offspring distribution; (iv) the endemic prevalence of infection; and (v) the transient dynamics of the process. We utilize these methods to explore a wide region of parameter space appropriate for human infectious diseases. We then extend these results to consider the effects of more realistic gamma-distributed infectious periods. We discuss how all these results differ from standard homogeneous-mixing models and assess the implications for the invasion, transmission and persistence of infection. The computational efficiency of the methodology presented here will hopefully aid in the parameterisation of structured models and in the evaluation of appropriate responses for future disease outbreaks