For more information about this meeting, contact Manfred Denker.

Title: | Utility maximation and (F)BSDE of quadratic growth |

Seminar: | Seminar on Probability and its Application |

Speaker: | Peter Imkeller, Humboldt University Berlin |

Abstract: |

A financial market model is considered on which agents (e.g. insurers) are
subject to an exogenous financial risk, which they trade by issuing a risk
bond. They are able to invest in a market asset correlated with the
exogenous risk. We investigate their utility maximization problem, and
calculate bond prices using utility indifference. In the case of
exponential utility, this hedging concept is interpreted by means of
martingale optimality, and solved with BSDE with drivers of quadratic
growth in the control variable.
For more general utility functions defined on the whole real line we show
that if an optimal strategy exists then it is given in terms of the
solution $(X,Y,Z)$ of a fully coupled FBSDE. Conversely if the FBSDE admits
a solution $(X,Y,Z)$ then an optimal strategy can be obtained. In the
complete market case, an assumption on the risk aversion guarantees that
the FBSDE admits a solution for any finite time horizon. As a particular
example of our approach we recover the BSDE for exponential utility, and
are able to treat non-classical utility functions like the sum of
exponential ones.
For utility functions defined on the half line we also reduce the
maximization problem to the solution of FBSDE connected with the ones
obtained by Peng (1993). In complete markets, once again we provide
conditions for solvability that are applicable to the power, the
logarithmic and some non-classical utilities. In our approach we propose an
alternative form of the maximum principle for which the Hamiltonian is
reflected in a remarkable martingale. This is joint work with U. Horst, Y.
Hu, A. R\'eveillac, and J. Zhang. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 11 / 04 / 2011 |

Time: | 02:20pm - 03:20pm |