Peter Imkeller

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In this paper, we consider a security market in which two investors on different information levels maximize their expected logarithmic utility from terminal wealth. While the ordinary investor’s portfolio decisions are based on a public information flow, the insider possesses from the beginning extra information about the outcome of some random variable G,(More)
We introduce a general continuous–time model for an illiquid financial market where the trades of a single large investor can move market prices. The model is specified in terms of parameter dependent semimartingales, and its mathematical analysis relies on the non–linear integration theory of such semimartingale families. The Itô–Wentzell formula is used(More)
We consider backward stochastic differential equations with drivers of quadratic growth (qgBSDE). We prove several statements concerning path regularity and stochastic smoothness of the solution processes of the qgBSDE, in particular we prove an extension of Zhang’s path regularity theorem to the quadratic growth setting. We give explicit convergence rates(More)
This thesis deals with the theory of so called forward-backward stochastic differential equations (FBSDE) which can be seen as a stochastic formulation and in some sense generalization of parabolic quasi-linear partial differential equations. The thesis consist of two parts: In the first we develop the theory of so called decoupling fields for general(More)
Let u(t; x); t 2 R; be an adapted process parametrized by a variable x in some metric space X, (!; dx) a probability kernel on the product of the probability space and the Borel sets of X. We deal with the question whether the Stratonovich integral of u(:; x) with respect to a Wiener process on and the integral of u(t; :) with respect to the random measure(More)
We consider families of random dynamical systems induced by parametrized one dimensional stochastic diierential equations. We give necessary and suucient conditions on the invariant measures of the associated Markov semigroups which ensure a stochastic bifurcation. This leads to suucient conditions on drift and diiusion coeecients for a stochastic pitchfork(More)
We review a general mathematical link between utility and information theory appearing in a simple financial market model with two kinds of small investors: insiders, whose extra information is stored in an enlargement of the less informed agents’ filtration. The insider’s expected logarithmic utility increment is described in terms of the information(More)
In this paper we deal with the utility maximization problem with a general utility function. We derive a new approach in which we reduce the utility maximization problem with general utility to the study of a fully-coupled Forward-Backward Stochastic Differential Equation (FBSDE). AMS Subject Classification: Primary 60H10, 93E20 JEL Classification: C61,(More)