The risk sensitive dynamic accumulation model and optimal pension saving management
PhD thesis advisor:
PhD thesis - Full text
This dissertation thesis analyses solutions to a fully non-linear
Hamilton-Jacobi-Bellman equation arising from the problem of optimal investment portfolio
that encounters a risk sensitive future pensioner, a typical participant of
the private defined-contribution based Second pillar of the Slovak pension
We show how the Hamilton-Jacobi-Bellman equation can be converted using the
Riccati transform into a Cauchy-type quasi-linear parabolic differential
and solve the associated parametric convex optimization problem. The weak
to the studied problem is approached by its double asymptotic expansion
with respect to small model parameters and utilized to build the analytical
which serves us to estimate the investor's optimal pension fund selection
We provide the analysis of the optimal policy from qualitative as well as
point of view and formulate main policy implications and recommendations
that are applicable for all policy makers, pension fund managers, and the
Finally, we bring to model to Slovak data and illustrate how the optimal
strategies and saver's expected terminal wealth accumulated on his/her
account change depending on model calibration and its key parameters.
 Macová, Z. and Ševčovič, D. (2010). Weakly nonlinear analysis of the
Hamilton-Jacobi-Bellman equation arising from pension savings management.
International Journal of Numerical Analysis and Modeling, 1:1-20.
 Z. Múčka, (2013). The optimal decision strategy in the second pillar of
the Slovak pension system. In Impacts of Aeging on Public Finance and Labour Markets in
EU Region, volume 1, pages 67-84, Bratislava. OECD & Institute of Economic Research SAS.