Market Consistent Pricing of Insurance Products

We present the first step in a program to develop a comprehensive, unified equilibrium theory of asset and liability pricing. We give a mathematical framework for pricing insurance products in a multiperiod financial market. This framework reflects classical economic principles (like utility maximization) and generates pricing algorithms for non-hedgeable insurance risk

Analyticity and uniform stability in the inverse spectral problem for Dirac operators

We prove that the inverse spectral mapping reconstructing the square integrable potentials on [0,1] of Dirac operators in the AKNS form from their spectral data (two spectra or one spectrum and the corresponding norming constants) is analytic and uniformly stable in a certain sense.Comment: 19 page

Multiplicative point process as a model of trading activity

Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper we generalize the model of interevent time to reproduce a variety of self-affine time series exhibiting power spectral density S(f) scaling as a power of the frequency f. Furthermore, we analyze the relation between the power-law correlations and the origin of the power-law probability distribution of the signal intensity. We introduce a stochastic multiplicative model for the time intervals between point events and analyze the statistical properties of the signal analytically and numerically. Such model system exhibits power-law spectral density S(f)~1/f**beta for various values of beta, including beta=1/2, 1 and 3/2. Explicit expressions for the power spectra in the low frequency limit and for the distribution density of the interevent time are obtained. The counting statistics of the events is analyzed analytically and numerically, as well. The specific interest of our analysis is related with the financial markets, where long-range correlations of price fluctuations largely depend on the number of transactions. We analyze the spectral density and counting statistics of the number of transactions. The model reproduces spectral properties of the real markets and explains the mechanism of power-law distribution of trading activity. The study provides evidence that the statistical properties of the financial markets are enclosed in the statistics of the time interval between trades. A multiplicative point process serves as a consistent model generating this statistics.Comment: 10 pages, 3 figure

Inverse spectral problems for Dirac operators with summable matrix-valued potentials

We consider the direct and inverse spectral problems for Dirac operators on $(0,1)$ with matrix-valued potentials whose entries belong to $L_p(0,1)$, $p\in[1,\infty)$. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest a method for reconstructing the potential from the corresponding spectral data.Comment: 32 page

Boundary relations and generalized resolvents of symmetric operators

The Kre\u{\i}n-Naimark formula provides a parametrization of all selfadjoint exit space extensions of a, not necessarily densely defined, symmetric operator, in terms of maximal dissipative (in \dC_+) holomorphic linear relations on the parameter space (the so-called Nevanlinna families). The new notion of a boundary relation makes it possible to interpret these parameter families as Weyl families of boundary relations and to establish a simple coupling method to construct the generalized resolvents from the given parameter family. The general version of the coupling method is introduced and the role of boundary relations and their Weyl families for the Kre\u{\i}n-Naimark formula is investigated and explained.Comment: 47 page

Integrated Microfluidic Platform for Oral Diagnostics

While many point-of-care (POC) diagnostic methods have been developed for blood-borne analytes, development of saliva-based POC diagnostics is in its infancy. We have developed a portable microfluidic device for detection of potential biomarkers of periodontal disease in saliva. The device performs rapid microfluidic chip-based immunoassays (<3–10 min) with low sample volume requirements (10 ΜL) and appreciable sensitivity (nM–pM). Our microfluidic method facilitates hands-free saliva analysis by integrating sample pretreatment (filtering, enrichment, mixing) with electrophoretic immunoassays to quickly measure analyte concentrations in minimally pretreated saliva samples. The microfluidic chip has been integrated with miniaturized electronics, optical elements, such as diode lasers, fluid-handling components, and data acquisition software to develop a portable, self-contained device. The device and methods are being tested by detecting potential biomarkers in saliva samples from patients diagnosed with periodontal disease. Our microchip-based analysis can readily be extended to detection of biomarkers of other diseases, both oral and systemic, in saliva and other oral fluids.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73594/1/annals.1384.004.pd