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In the Black-Scholes type financial market, the risky asset S 1 ( ) is supposed to satisfy dS 1 ( t ) = S 1 ( t )( b ( t ) dt + Sigma ( t ) dW ( t ) where W ( ) is a Brownian motion. The processes b ( ), Sigma ( ) are progressively measurable with respect to the filtration generated by W ( ). They are known as the mean rate of return and the volatility respectively. A portfolio is described by a progressively measurable processes Pi1 ( ), where Pi1 ( t ) gives the amount invested in the risky asset at the time t. Typically, the optimal portfolio Pi1 ( ) (that, which maximizes the expected utility), depends at the time t, among other quantities, on b ( t ) meaning that the mean rate of return shall be known in order to follow the optimal trading strategy. However, in a real-world market, no direct observation of this quantity is possible since the available information comes from the behavior of the stock prices which gives a noisy observation of b ( ). In the present work, we consider the optimal portfolio selection which uses only the observation of stock prices.

We discuss the analytic properties of AdS scalar exchange graphs in the crossed channel. We show that the possible non-analytic terms drop out by virtue of non-trivial properties of generalized hypergeometric functions. The absence of non-analytic terms is a necessary condition for the existence of an operator product expansion for CFT amplitudes obtained from AdS/CFT correspondence.

Linearized flows past slender bodies can be asymptotically described by a linear Fredholm integral equation. A collocation method to solve this equation is presented. In cases where the spectral representation of the integral operator is explicitly known, the collocation method recovers the spectrum of the continuous operator. The approximation error is estimated for two discretizations of the integral operator and the convergence is proved. The collocation scheme is validated in several test cases and extended to situations where the spectrum is not explicit.

We consider investment problems where an investor can invest in a savings account, stocks and bonds and tries to maximize her utility from terminal wealth. In contrast to the classical Merton problem we assume a stochastic interest rate. To solve the corresponding control problems it is necessary to prove averi cation theorem without the usual Lipschitz assumptions.

Abstract: It has recently been shown that the equation of motion of a massless scalar field in the background of some specific p branes can be reduced to a modified Mathieu equation. In the following the absorption rate of the scalar by a D3 brane in ten dimensions is calculated in terms of modified Mathieu functions of the first kind, using standard Mathieu coefficients. The relation of the latter to Dougall coefficients (used by others) is investigated. The S-matrix obtained in terms of modified Mathieu functions of the first kind is easily evaluated if known rapidly convergent low energy expansions of these in terms of products of Bessel functions are used. Leading order terms, including the interesting logarithmic contributions, can be obtained analytically.

Abstract: We develop a method of singularity analysis for conformal graphs which, in particular, is applicable to the holographic image of AdS supergravity theory. It can be used to determine the critical exponents for any such graph in a given channel. These exponents determine the towers of conformal blocks that are exchanged in this channel. We analyze the scalar AdS box graph and show that it has the same critical exponents as the corresponding CFT box graph. Thus pairs of external fields couple to the same exchanged conformal blocks in both theories. This is looked upon as a general structural argument supporting the Maldacena hypothesis.

This paper provides an annotated bibliography of multiple objective combinatorial optimization, MOCO. We present a general formulation of MOCO problems, describe the main characteristics of MOCO problems, and review the main properties and theoretical results for these problems. One section is devoted to a brief description of the available solution methodology, both exact and heuristic. The main part of the paper is devoted to an annotation of the existing literature in the field organized problem by problem. We conclude the paper by stating open questions and areas of future research. The list of references comprises more than 350 entries.

We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT correspondence. We study the scalar exchange graphs in AdS and discuss their analytic properties. Using methods of conformal partial wave analysis, we present a general procedure to study conformal four-point functions in terms of exchanges of scalar and tensor fields. The logarithmic terms in the four-point functions are connected to the anomalous dimensions of the exchanged fields. Comparison of the results from AdS graphs with the conformal partial wave analysis, suggests a possible general form for the operator product expansion of scalar fields in the boundary CFT.

The satellite-to-satellite tracking (SST) problems are characterized from mathematical point of view. Uniqueness results are formulated. Moreover, the basic relations are developed between (scalar) approximation of the earth's gravitational potential by "scalar basis systems" and (vectorial) approximation of the gravitational eld by "vectorial basis systems". Finally, the mathematical justication is given for approximating the external geopotential field by finite linear combinations of certain gradient fields (for example, gradient fields of multi-poles) consistent to a given set of SST data.

Wir beschreiben eine Methode zur Approximation von Spannungsgradienten aus diskreten Spannungsdaten. Eine herkömmliche Diskretisierung der Ableitungen aus Funktionswerten führt zu Stabilitätsproblemen, weswegen eine Möglichkeit zur Kontrolle der Ableitungen notwendig ist (Regularisierung). Wir bestimmen zunächst das Funktional der potentiellen Energie und führen zusätzlich ein Fehlerfunktional ein, das die Anpassung an die vorgegebenen diskreten Werte ermöglicht. Durch Gewichtung der beiden Funktionale und Minimierung des Gesamtfunktionals erhält man den gewünschten Ausgleich zwischen der Fehlerkontrolle beim Ableiten einerseits und Kontrolle der Fehler bei den Randwerten andererseits.