SEMINARIO DI
FINANZA
MATEMATICA
ore
11.30
Scuola Normale
Superiore
Pisa
(Aula
Bianchi)
Fausto
GOZZI
Luiss,
Roma
Terrà un seminario dal
titolo:
“Assel Liabilit Management for Pension Funds: a
Stochastic Control Approach”
Abstract
In
this talk we propose and study a continuous time stochastic model of optimal
allocation for a defined contribution pension fund with a minimum guarantee. We
adopt the point of view of a fund manager maximizing the expected utility from
the fund wealth over an infinite horizon.
In
our model the dynamics of wealth takes directly into account the flows of
contributions and benefits and the level of wealth is constrained to stay above
a ``solvency level''. The fund manager can invest in a riskless asset and in a
risky asset but borrowing and short selling are prohibited. The model is
naturally formulated as an optimal stochastic control problem that have some
similarities with similar to Merton's optimal portfolio
problems.
The
main technical issues that render this problem difficult are:- the presence of
state constraints, motivated by the prescription of the "solvency level".- the
presence of delay terms (the so-called "surplus") in the state equation, due to
the standard form of the contract (the pension give to the subscribers depends
on the past performance of the fund).
First
we concentrate first the analysis on the effect of the solvency constraint,
analyzing in particular what happens when the fund wealth reaches the allowed
minimum value represented by the solvency level. Here we show that the value
function of the problem is a regular solution of the associated
Hamilton-Jacobi-Bellman equation. Then we apply verification techniques to get
the optimal allocation strategy in feedback form and to study its properties. We
finally give a special example with explicit solution.
Second
we consider the problem where also the "surplus" is present. This problem is
naturally infinite dimensional and is much more difficult. We present here the
ideas used to approach it and some first partial results.
Tutti gli interessati
sono invitati a partecipare.
SAD
Classe
di Scienze