Michael Kohlmann

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We obtain the global existence and uniqueness result for a one-dimensional backward stochastic Riccati equation, whose generator contains a quadratic term of L (the second unknown component). This solves the one-dimensional case of Bismut-Peng's problem which w as initially proposed by Bismut (1978) in the Springer yellow book LNM 649. We use an(More)
We discuss optimal portfolio selection with respect to utility functions of type −e −αx , α > 0 (exponential problem) and −|1 − αx p | p (p-th problem). We consider N risky assets and a risk-free bond. Risky assets are modeled by continuous semimartingales or exponential Lévy processes. These dynamic expected utility maximization problems are solved by(More)
Zusammenfassung Die vorliegende Arbeit befasst sich mit linear isoelastischen stochastischen Kontrollprob-lemen. Es handelt sich hierbei um die Aufgabe, für ein festes q > 1 das Kostenfunktional J(u) = 1 q E[ T τ Q(s)|x(s)| q + N (s)|u(s)| q ds + M |x(T)| q ] ¨ uber u zu minimieren, wobei die Kontrollvariable u aus einem Vektorraum U stochastischer Prozesse(More)
It is well known that backward stochastic diierential equations BSDEs stem from the study on the Pontryagin type maximum principle for optimal stochastic controls. A solution of a BSDE hits a given terminal value which is a random variable by virtue of an additional martingale term and an indeenite initial state. This paper attempts to view the relation(More)