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)
We prove an existence and uniqueness theorem for backward stochastic diierential equations driven by a Brownian motion, where the uniform Lipschitz continuity is replaced by a stochastic one.
The existence of an adapted solution to a backward stochastic differential equation which is not adapted to the ltration of the underlying Brownian motion is proved. This result is applied to the pricing of contingent claims. It allows to compare the prices of agents who have diierent information about the evolution of the market. The problem is considered… (More)
We review the relations between adjoints of stochastic control problems with the derivative of the value function, and the latter with the value function of a stopping problem. These results are applied to the pricing of contingent claims. 1. Introduction In kohh we examined the properties of adjoint processes in stochas-tic control on the basis of the… (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)