The risk sensitive dynamic accumulation model and optimal pension saving management
Zuzana Múčka
PhD thesis advisor: Daniel Ševčovič,

PhD thesis - Full text   

Summary: This dissertation thesis analyses solutions to a fully non-linear Hamilton-Jacobi-Bellman equation arising from the problem of optimal investment portfolio construction that encounters a risk sensitive future pensioner, a typical participant of the private defined-contribution based Second pillar of the Slovak pension system. We show how the Hamilton-Jacobi-Bellman equation can be converted using the Riccati transform into a Cauchy-type quasi-linear parabolic differential equation and solve the associated parametric convex optimization problem. The weak solution to the studied problem is approached by its double asymptotic expansion with respect to small model parameters and utilized to build the analytical model which serves us to estimate the investor's optimal pension fund selection strategy. We provide the analysis of the optimal policy from qualitative as well as quantitative point of view and formulate main policy implications and recommendations that are applicable for all policy makers, pension fund managers, and the Second pillar participants. Finally, we bring to model to Slovak data and illustrate how the optimal investment strategies and saver's expected terminal wealth accumulated on his/her pension account change depending on model calibration and its key parameters.
Related papers
[1] 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. PDF file   

[2] 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.