Optimal Insurance Purchase Strategies via Optimal Multiple Stopping Times

Targino, Rodrigo S.; Peters, Gareth W.; Sofronov, Georgy; Shevchenko, Pavel V.

doi:10.2139/ssrn.2505973

Cited by 3 publications

(9 citation statements)

References 27 publications

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“…We develop three different series expansion methods for representing the marginal likelihood using orthogonal basis functions [44], [45]. We will show how these expansions are applicable under different scenarios.…”

Section: Probability Density Approximation Via Series Expansion Mmentioning

confidence: 99%

“…All of these series expansion methods use the basic properties of orthogonality between density functions and polynomials. This property guarantees the integration of density to be equal to one [44], [45]. Each of these series expansion has different properties and different supports.…”

Section: Probability Density Approximation Via Series Expansion Mmentioning

confidence: 99%

“…It is therefore important to characterize these values that produce the "envelope" for the density approximation in which it will remain positive. This characterization can be carried out by finding the appropriate regions in the Skew-Kurtosis plane (S-K plane) which generate positive support [44], [45].…”

Section: Probability Density Approximation Via Series Expansion Mmentioning

confidence: 99%

“…The Gamma-Laguerre series expansion approximates a probability distribution, f Y (y), by utilising the orthogonality between the Gamma density kernel and the Laguerre polynomials in order to obtain an efficient series expansion [45]. In contrast to the Gram-Charlier series expansion where the Hermite polynomials have support on the entire real line, the Laguerre polynomials only have support on the positive real line y ∈ R + .…”

Section: B Gamma-laguerre Series Expansionmentioning

confidence: 99%

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Event Detection in Wireless Sensor Networks in Random Spatial Sensors Deployments

Zhang

Peters

Xiao

et al. 2015

IEEE Trans. Signal Process.

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We develop a new class of event detection algorithms in Wireless Sensor Networks where the sensors are randomly deployed spatially. We formulate the detection problem as a binary hypothesis testing problem and design the optimal decision rules for two scenarios, namely the Poisson Point Process and Binomial Point Process random deployments. To calculate the intractable marginal likelihood density, we develop three types of series expansion methods which are based on an Askey-orthogonal polynomials. In addition, we develop a novel framework to provide guidance on which series expansion is most suitable (i.e., most accurate) to use for different system parameters. Extensive Monte Carlo simulations are carried out to illustrate the benefits of this framework as well as the quality of the series expansion methods, and the impacts that different parameters have on detection performance via the Receiver Operating Curves (ROC).

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Section: Probability Density Approximation Via Series Expansion Mmentioning

confidence: 99%

Section: Probability Density Approximation Via Series Expansion Mmentioning

confidence: 99%

Section: Probability Density Approximation Via Series Expansion Mmentioning

confidence: 99%

Section: B Gamma-laguerre Series Expansionmentioning

confidence: 99%

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Event Detection in Wireless Sensor Networks in Random Spatial Sensors Deployments

Zhang

Peters

Xiao

et al. 2015

IEEE Trans. Signal Process.

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“…In order to evaluate the marginal likelihood in (5.8), we derive novel approximations for the marginal likelihood. We develop three different series expansion methods for representing the marginal likelihood using orthogonal basis functions [73,125]. We will show how these The respective Askey polynomials [126] are Hermite polynomials, Laguerre polynomials and Jacobi polynomials.…”

Section: Probability Density Approximation Via Series Expansion Methodsmentioning

confidence: 99%

Studies of networking algorithms in wireless sensor networks

Zhang¹

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In traditional wireless sensor networks (WSNs), sensors powered by battery are largely deployed in a field to observe certain physical phenomena, such as temperature, noise and many more. The purpose of WSN is to be able to sense from environment and detect events for a long time. By improving the network lifetime, WSNs are able to detect events longer. This agrees with the nature of WSNs, which is sense-to-detect events through long operations (hopefully) I would like to express my sincere thanks and appreciation to my supervisor, Prof. Xiao Gaoxi (NTU), and co-supervisor, Dr. Tan Hwee Pink (I 2 R) for their invaluable guidance, support and suggestions. Their knowledge, suggestions, and discussions have helped me become a capable researcher. Their encouragement also helped me to overcome the difficulties encountered in my research. I also want to thank my colleagues in Sense & Sense-ability lab of I 2 R, for their generous help. I want to thank Dr. Ido Nevat for his explanation of the statistical modeling, I also want to thank Dr. Gareth Peters from University of College London for the valuable discussions and contributions towards my papers. I also want to thank Lin Shaowei and Jing Yang for helping me discuss problem and revise papers. My gratitude also goes to Pius Lee, Jin Yunye, Wong Liangze for their friendship and support. I am very grateful to the members of our Infinitus Lab in NTU. It is a pleasure to collaborate with my teammate, Yu Yi. I am also indebted to my friend Zhang Li, for his technical and personal suggestions, especially for his help on PPT slides.

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